A Study of
Mandatory Engine Maintenance
for Reducing Vehicle Exhaust Emissions
Volume III. A Documentation Handbook for
the Economic Effectiveness Model
Year End Report
July 1972
In Support of:
APRAC Project Number CAPE-13-68
for
Coordinating Research Council. Inc.
Thirty Rockefeller Plaza
New York. New York 10020
TRW
SYSTfMS GROUP
ONE SP*C£ PARK ' REDONDO BEACH CALIFORNIA 902'8
and
Environmental Protection Agency
Air Pollution Control Office
5600 Fishers Lane
Rockville. Maryland 20852
SCOTT RESEARCH LABORATORIES, INC
P. O. BOX X4I«
SAN BERNARDINO. CALIFORNIA U4O«
-------
A Study of
Mandatory Engine Maintenance
for Reducing Vehicle Exhaust Emissions
Volume III. A Documentation Handbook for
the Economic Effectiveness Model
Year End Report
July 1972
In Support of:
APRAC Project Number CAPE-13-68
for
Coordinating Research Council. Inc.
Thirty Rockefeller Plaza
New York. New York 10020
TRW
srsrcMS enouf
ONI S**Cl Hm HfOOMOO Sf'Cx CtilfOHHI* 907/«
and
Environmental Protection Agency
Air Pollution Control Office
5600 Fishers Lane
Rockville. Maryland 20852
SCOTT RESEARCH LABORATORIES. INC
f, O. BOX Ml*
AN BERNARDINO. CALIFORNIA B4O«
-------
PREFACE
This report, "A Study of Mandatory Engine Maintenance for Reducing
Vehicle Exhaust Emissions," consists of six volumes. The following are
the subtitles given for each volume:
Executive Summary, Volume I
t Mandatory Inspection/Maintenance Systems Study, Volume II
A Documentation Handbook for the Economic Effectiveness
Model, Volume III
Experimental Characterization of Vehicle Emissions and
Maintenance States, Volume IV
a Experimental Characterization of Service Organization
Maintenance Performance, Volume V
a A Comparison of Oxides of Nitrogen Measurements Made With
Chemiluminescent and Non-Dispersive Radiation Analyzers,
Volume VI
The first volume summarizes the general objectives, approach and
results of the study. The second volume presents the results of the
mandatory inspection/maintenance system study conducted with a computer-
ized system model which is described in Volume III. The experimental
programs conducted to develop input data for the model are described in
Volume IV (Interim Report of 1971-72 Test Effort) and V. Volume VI pre-
sents comparative measurements of NO and NO using chemiluminescence and
X
NDIR/NDUV instruments and differences in these measurements are examined.
The work presented herein is the product of a joint effort by TRW
Systems Group and its subcontractor, Scott Research Laboratories. TRW,
as the prime contractor, was responsible for overall program management,
experimental design, data management and analysis, and the economic
effectiveness study. Scott acquired and tested all of the study vehicles.
Scott also provided technical assistance in selecting emission test pro-
cedures and in evaluating the test results.
-------
ECONOMIC EFFECTIVENESS MODEL DOCUMENTATION
TABLE OF CONTENTS
1.0 INTRODUCTION 1
1.1 Purpose 1
1.2 Background 2
1.3 Conceptual Framework and Process 4
1.4 Methodological Approach 7
1.5 Computer Program Design 9
2.0 PROGRAM SPECIFICATION 11
2.1 Policy Evaluation 11
2.1.1 Inspection Strategies 12
2.1.2 System Constraints 17
2.2 System Design 18
3.0 ECONOMIC EFFECTIVENESS MODEL 20
3.1 System Overview 20
3.2 Vehicle Emission Models 22
3.2.1 Inspection Models 24
3.2.2 Deterioration of Parameters and Emission Modes 28
3.2.3 Effectiveness of Maintenance 29
3.2.4 Reliability of Maintenance 31
3.2.5 Baseline Emission Prediction 33
3.3 Economic Analysis Model 35
3.3.1 Outline of Economic Model 36
3.3.2 Major Elements of the Model 36
3.3.3 The Effect of Time on Cost 40
3.3.4 Other Economic Factors 41
3.3.5 Total System Cost 43
3.4 Operations Research Model 44
3.5 Statistical Model 46
3.6 Utility Models 51
11
-------
TABLE OF CONTENTS (Con't)
3.7 Decision Criterion 53
4.0 ANALYTICAL METHODS OF SOLUTION -55
4.1 Simulation 55
4.2 Optimization 56
4.2.1 General Optimization Methodology 56
4.2.2 Linear Programming Algorithm 57
4.3 Sensitivity Analysis 60
4.3.1 Model Structure 61
4.3.2 Program Variables . 61
4.3.3 Empirical Data 62
4.3.4 Regional Evaluation . 62
APPENDIX A Study Ground Rules and Assumptions 53
APPENDIX B Model Limitations 66
APPENDIX C Input/Output Features of the Exonomic
Effectiveness Computer Model 68
C.I Introduction 68
C.2 Input Options . 70
C.3 Output Capabilities 79
APPENDIX D Ancillary Model Data -81
REFERENCES 85
-------
LIST OF FIGURES
Figure Page
1-1 Vehicle Inspection/Maintenance Process 5
1-2 Model Design Overview 8
1-3 Economic Effectiveness Processor 10
2-1 Functional Elements of Inspection/ 13
Maintenance
3-1 Model Schematic 21
3-2 Basic Components of Process 23
3-3 Relationship Between Mode Emissions and 28
Engine Component Distributions
3-4 Parametric and Emission Maintenance and 32
Deterioration Effects
3-5 Cost Estimator Module 37
3-6 Economic Effectiveness Statisticsl Model 47
1v
-------
LIST OF TABLES
Table Page
2-1 Maintenance Options Available Within the Economic
Effectiveness Model 16
3-1 Parameter/Mode Categories 25
C-l Inspection Maintenance Procedure Options 71
C-2 Regional Options and Data Requirements 73
C-3 System Operational and Design Variables 74
C-4 Flow Schematic of Input Options and Data
Requirements 75
C-5 Required Input for an Engine Inspection/Maintenance
Procedure 78
C-6 Economic Effectiveness Summary Printout 80
D-l Effectiveness of Voluntary Maintenance 82
D-2 Inspection/Maintenance Cost Components 83
D-3 Miscellaneous Data 84
-------
1.0 INTRODUCTION
1.1 PURPOSE
The primary purpose of the Economic Effectiveness Model is to serve
as a research and design tool for assessing the various implications of
a mandatory program of vehicle inspection/maintenance. As such, it has
been constructed with the capability to evaluate a wide range of possible
procedure and design alternatives. The model is designed to both analyze
the regional feasibility of vehicle inspection/maintenance as well as to
specify an optimal system design. Input data for several regional areas
covering the gamut of auto related air quality problems are incorpor-
ated into the model.
In addition to these functions, the model can also be used to
analyze the sensitivity of system performance to various model assumptions
and basic data inputs. Used in this way the model serves as a "self
regulating device" for identifying areas requiring further analytical and
empirical definition. The model by its very nature is policy oriented.
That is, it is best used for evaluating the attractiveness of alternative
policies, e.g., engine inspection or emission inspection, which govern
and control the operation of an inspection/maintenance system. Actually,
there exists a hierarchy of policy decision variables within the structure
of the model. The determination of the optimal values for these variables
is presently accomplished through the use of a para-optimization technique.
The main function of the model, in addition to analyzing policy
variables, is in simulating the behavior of the inspection/maintenance
process over time. Here, the economic-effectiveness of various strategies
can be measured in terms of emission reductions and program costs at each
time interval. A statistical analysis of these reductions can be under-
taken as a further check on predicted model performance. The final
step in this process is to utilize the unadjusted or statistically
adjusted figure of merit for selecting the optimal model design for
each candidate region.
-------
1.2 BACKGROUND
A mandatory program of vehicle inspection/maintenance represents one
short term approach for controlling exhaust emissions from automobiles.
Such a program has the advantage of effecting most vehicles within the
population fleet. The underlying principle governing the operation of
an inspection/maintenance program is as follows:
"Reductions in a vehicle's exhaust emissions can be achieved
through the adjustment and/or replacement of a specific set
of engine block components."
Obviously, there exists a number of fundamental questions concerning the
feasibility of a mandatory program. Among the more important ones are:
(1) What is the range of expected emission reductions achievable
from the various maintenance treatments?
(2) What are the costs associated with each of these programs?
(3) What is the impact of regional variations on overall program
effectiveness and procedure selection?
(4) How is program effectiveness likely to change with time and
new control technology?
The development of the economic-effectiveness computer program represents
an attempt to answer these questions. It provides a flexible tool
for examining in an accurate and detailed manner the various alternatives
which form the underpinnings of this control concept.
Automotive emission control through a program of inspection/main-
tenance can be accomplished by employing any one of a number of available
options. However, there are in the limit two classes of inspection
procedures which embody the entire range of possible alternatives. They
are:
o Direct measurement of the state of selected engine block components
using conventional or more sophisticated garage-type equipment.
o Indirect measurement of the state of selected engine block compo-
nents using engine exhaust emission levels (signatures) under
varying load conditions.
-------
Each basic alternative has a number of distinct advantages and disadvantages,
In the case of the direct approach, the chief benefit is in its ability to
maximize potential emission reductions. Here, engine block components are
adjusted and/or replaced based on a direct diagnosis of the engine state.
The margin for error, in terms of omissions and commissions,is relatively
small. The main disadvantage lies with the higher operating costs required
for such a program. This type of program would normally be conducted in
a franchised or certified, privately owned garage.
The indirect or emission inspection approach is more sophisticated
in terms of both procedure techniques and equipment specifications.
Hydrocarbon, carbon monoxide and NOX emission measurements are made at
several engine loadings. An analysis of these "mode" emission levels
leads to the identification of faulty engine components. Although the
costs for such a program are generally lower than for the direct approach,
the resultant emission reductions are also smaller. This is due primarily
to the higher incidence of inspection errors encountered in actual
operation. The inspection portion of this approach is best performed in a
state operated facility, whereas the maintenance treatment should be
undertaken in a conventional franchised garage.
Embodied within each of these basic alternatives is an endless number
of sub-strategies and system variations. Selection of the optimal policy
set, therefore, entails a systematic tradeoff of the relevant program
variables. One function of the model is to evaluate analytically the
tradeoff implications of various variable sets. The following section
presents a simplified overview on the structure and process of a vehicle
inspection/maintenance program.
-------
1.3 CONCEPTUAL FRAMEWORK AND PROCESS
A mandatory program of vehicle inspection maintenance can be viewed
as a process with a fixed number of specific steps. The first step
involves the inspection, either direct or indirect, of all vehicles within
a given population. The inspection procedure is based on measuring the
state of the engine, e.g., engine components and emission levels, and
comparing these results with some prescribed criteria. If the measured
value falls outside the allowable range, then the vehicle must undergo
a specified maintenance treatment. Those vehicles passing the test are
free to go without further involvement in the process. This cycle is
repeated on a periodic basis over the time horizon of the program.
Because of engine system deterioration, most vehicles will eventually
undergo some form of maintenance treatment.
Figure 1-1 presents a schematic overview of the inspection/maintenance
process for an emission inspection approach. Between inspection intervals
a vehicle's exhaust emissions will normally rise due to the deteriora-
tion and/or malfunction of various engine block components. Thus, vehicles
passing the initial test may in fact fail subsequent inspections. The
converse is the case for many automobiles which failed the initial
examination. Undergoing a selected maintenance treatment, the average
vehicle should pass the next test assuming the criteria has remained
invariant.
The conceptual structure of a vehicle inspection/maintenance program
consists of three fundamental components:
o Engineering Design
o Economic Factors
o Regional Data
Their interaction must be clearly understood in order to select the system
design elements which yield optimal performance and cost. The factors of
engineering design fall into two basic categories: (1) type of inspection/
maintenance procedure and (2) facilities configuration. The cost of each
candidate system must be computed in order to arrive at the program's
overall effectiveness. The relevant costs here are composed of capital,
-------
VEHICLE INSPECTION MAINTENANCE PROCESS
INSPECTION STATION
[RE'PA\K_ SHO_P_
FAIL
PASS
LOW EMISSIONS
TIME
MEDIUM EMISSIONS
INSPECTION STATION
^>Mg>
LOW EMISSIONS MEDIUM EMISSIONS
HIGH EMISSIONS
FIRURE 1-1 VEHICLE INSPECTION/MAINTENANCE PROCESS
-------
labor and user inconvenience. Regional constraints take the form of air
quality standards, minimum acceptable emission reductions, and maximum
cost expenditures. Any viable program of inspection/maintenance should
fall within these stated limits.
While emission reduction performance provides some insight into the
feasibility of vehicle inspection/maintenance with respect to other control
concepts, some function of both performance and costs is required in
selecting the optimal system design. Unfortunately, no one function,
i.e., figure of merit, appears to embody all of the characteristics
desired in selecting from between the several alternatives. The most
relevant figure of merit and the one incorporated in the Economic
Effectiveness model consists of discounted total program cost divided
by the weighted species emission reductions achieved over the time horizon
of the program. Alternatively, the emission reductions at some future
point in time may also be selected for calculating the figure of merit.
In addition to procedure selection, this figure of merit can also be
used for determining the optimal values of the policy variables which
unite the various elements of the system. A partial list of these variables
is given below:
t Interval between inspections
t Pass/fail inspection criteria
Extent of maintenance treatment
t Facilities configuration
To better understand the behavior of an inspection/maintenance
system over time required the development of a mathematical computer
model. Given in the next two sections is a discussion of analytical
approach taken in designing the model and in constructing the Economic
Effectiveness Computer Program.
-------
1.4 METHODOLOGICAL APPROACH
The methodological approach adopted for constructing the Economic
Effectiveness model involved a blending of theoretical and empirical
relationships. The theory provided the conceptual framework for describing
the inspection/maintenance process whereas the experimental data yielded
the specific transformations needed to define and interconnect the various
model elements.
The development of the model required a detailed specification of
the various relationships characterizing the Inspection/Maintenance Pro-
cess. Figure 1-2 shows schematically the salient components constituting
the present model. The three main components -- engineering design,
economic analysis and regional characterization form the core or nucleus
of the inspection/maintenance model. Each of these components describes or
delineates one fundamental aspect of the total process. How these
interact must be clearly understood so that system design factors are
selected in combinations to yield optimal cost and performance.
Attempting to describe a physical process with an abstract mathematical
model raises a number of technical problems. One important issue involves
the level of aggregation used in the model to characterize the actual
process. Use of a simulation model yields an effective vehicle for
coping with many of these questions. Here, basic study grounds and
model assumptions, e.g., level of aggregation, can be isolated and examined
in detail. As such, a simulation model strikes a good balance between a
strictly theoretical model and an empirical model. The simulation model
used in describing the inspection/maintenance process provides a powerful
tool not only for assessing the feasibility of this control approach but
also in developing an optimal system design specification. One phase of
such a feasibility assessment involves the evaluation of potential procedure
strategies, e.g., engine inspection. Within this context, the simulation
model can be used to measure the performance of these strategies over time
and under varying system constraints. The resultant model design provides
a great deal of flexibility yet contains sufficient depth to describe the
process in intimate detail.
-------
Physical
Description of
I/M Process and
System Configuration
CXI
Policy Alternatives
Economic Specification
of Capital Investment
Requirements and
Operating Cash Flows
Regional Data
o Vehicle Attributes
o Cost Factors
o Air Quality Standards
Economic Effectiveness
Model
t>f
At
Strategy
FIGURE 1-2 MODEL DESIGN OVERVIEW
-------
1.5 COMPUTER PROGRAM DESIGN
The development of a conceptual model represented only part of this
research effort. A second and equally important step involved the selection
of a method for operational izing the Economic Effectiveness Model. A
computer-based design approach provided the flexibility needed to accommo-
date the large data bank and to evaluate the multiplicity of system
tradeoffs.
The Economic Effectiveness Program has been coded in Fortran IV
and is presently operating on a CDC 6500 system. Due to its flexible
design, it can evaluate a wide range of potential strategies with little
or no change to the basic model structure or data bank. Simplicity and
flexibility are salient characteristics of the input language. The hub
of this input system is its "key word" translator. It is used to convert
literal phrases, e.g., idle or control fleet, into internal programming
code. As such, it greatly reduces the time required to setup a computer
run. An executive routine has also been added to check for input errors
and to control output.
The program also provides several levels of output depending on user
requirements. For standard cases, it outputs computer generated plots
of emission time histories, program figure of merit, emission reductions
and numerous accounting figures. For more detail information, a debug
option is available which prints the basic calcualtions from each of the
major subroutines. Figure 1-3 presents a schematic overview of the cur-
rent program.
The primary use of the program is in simulating the performance of
proposed inspection/maintenance procedures over a given time horizon.
The program can also be used to develop an optimal system design for
both a franchised garage and state-operated inspection station. Finally,
the program provides means for testing the significance of various types
of emissions data, arid for measuring the impact of basic study ground
rules.
-------
IDLE
r
CONTROL
INPUT
TRANSLATOR
AND
EXECUTIVE
SYSTEM
©Q
ECONOMIC EFFECTIVENESS
PROGRAM
OUTPUT
FIGURE OF
MERIT
EMISSION
TIME
HISTORIES
ECONOMIC EFFECTIVENESS PROCESSOR
FIGURE 1-3 ECONOMIC EFFECTIVENESS PROCESSOR
-------
2.0 PROGRAM SPECIFICATION
A mandatory program of vehicle inspection/maintenance embodies an
endless number of possible system alternatives. These options run the
gambit from policy decisions to instrumentation selection. This decision
hierarchy introduces a great deal of complexity into the basic evaluation
process. Such structural complexity becomes necessary, however, in order
to achieve a reasonable degree of precision in predicted outcomes.
The two fundamental aspects of developing a viable program specifi-
cation involve both procedure identification and system design. The first
one focuses on the evaluation of various policy alternatives in terms
of cost and effectiveness. The second is concerned with the overall rela-
tionships and interactions between the numerous components constituting the
system. Both of these aspects are detailed in great degree within the
Economic Effectiveness Model. Each one can be examined individually or
simultaneously depending on the particular application.
2.1 POLICY EVALUATION
The problem of ultimate concern is the use of the Economic Effective-
ness model in developing an optimal program of vehicle Inspection/Main-
tenance. This necessitates identification of all viable strategy options
and their systematic examination via the model. The basic policy options
available for examination in a program of vehicle inspection/maintenance
are procedure selection and method of operation (state lane or franchise
garage). Determination of the "best" procedure affords some insight into
the feasibility of this approach for reducing exhaust emissions. Design
of the optimal inspection/maintenance system will depend heavily on the
cost attractiveness of the method of operation. Each of these options
involves a number of potential variations. Selection of the optimal
policy set, therefore, entails a systematic tradeoff analysis of all
relevant variables and parameters. A quantitative measure of the effec-
tiveness of these policies can be obtained by employing the systems
framework embodied in the model.
n
-------
2.1.1 Inspection Strategies
Two basic inspection strategies are available within the context
of this control approach. These strategies must be both effective
(result in substantial emission reductions) and economical to implement
(lowest cost for the emission reductions achieved). A strategy as used
here implies a policy statement concerning (1) whether inspection faci-
lities are to be privately or publicly financed and operated; (2) what
the quantitative inspection criteria are; (3) the type of mandatory
maintenance to be performed in order to achieve the desired reductions
in each of the emission species.
State vs. Private Inspection
A number of inspection/maintenance procedures have been suggested
by other investigators. One of the purposes of the Economic-Effectiveness
study is to evaluate the efficacy of these procedures and to rank them
within a systematic framework. Methods of improving these procedures
and/or identifying new ones may then proceed. Basic inspection approaches
may generally be classified as to whether they are best applied in a
state inspection lane or in a franchised garage. The state inspections
generally imply a high process throughput and, therefore, sophisticated
diagnostic instrumentation and data management systems with large capital
expenditures. Typical of this strategy are approaches wherein
several engine attributes are measured which are known to be highly
correlated to engine maintenance state. The measurement of exhaust
emissions under engine operating modes or truncated driving cycles
typify this approach.
At the other end of the spectrum are those inspection approaches
which use conventional or upgraded diagnostic equipment to identify
engine malfunctions known to adversely influence exhaust emissions.
These approaches tend to be labor intensive rather than capital intensive
and are, therefore, more effectively applied in existing service organi-
zations where trained labor and commercial equipment are already available.
These are intermediate and special cases of interest, some of which may
be studied within the currently structured computer model.
12
-------
In order to select quantitative inspection criteria, the procedures
for inspecting and maintaining engine systems must first be broken into
their functional parts:
Screening
Subsystem inspection
Component diagnosis
t Maintenance
The screening test in the current environment of voluntary maintenance
is performed by the vehicle owner. He decides on the basis of mileage,
performance, or operability to have his vehicle maintained. In the latter
two cases, the service organization identifies the offending subsystems
usually relying heavily on judgmental and qualitative measurements. They
may then perform quantitative measurements on components or rely on
visually or acoustically sensed qualitative judgments on the state of
components and adjustments within the system, often concurrently with
the maintenance action. Ideally, one would wish to place these functional
elements on a more quantitative basis and, indeed, this is necessary
when adapting them to a state inspection. Of specific interest is the
determination of the extent to which it is economically feasible to
transfer detailed diagnostic activities previously associated with
voluntary maintenance to a state inspection process.
In Figure 2-1 generalized procedures are shown in which various
levels of diagnosis are transferred from what is routinely the maintenance
to the inspection activity.
INSPECTION -STA1C LANE MAINTENANCE - FKANCHISEt> GARAGE
OR
fASS
OR
PASS 1
^r 1 SCREENING
< TEST
FAIL
SCREENING
TEST
DETAILED
SUBSYSTEM
DIAGNOSIS
ASS
FAIL
SCREENING
TEST
'*'L DETAILED
DIAGNOSIS
DETAILED
SUBSYSTEM
DIAGNOSIS
DETAILED
^J COMPONENT
DIAGNOSIS
DETAILED
COMPONENT
DIAGNOSIS
fcj INDICATED
*" MAINTENANCE
--*
^
DETAILED
COMPONENT
DIAGNOSIS
INDICATED
MAINTENANCE
.^ INDICATED
* MAINTENANCE
Figure 2-1 Functional Elements of
Inspection/Maintenance
13
-------
An advantage of the above transfer would be that a detailed diagnosis
during the inspection process would completely eliminate diagnostic
decisions and errors during the maintenance treatment. Because
complex and possibly automated instrument systems are required to
perform such a diagnosis in a cost effective manner, it may be economical
to perform a screening test to limit the number of vehicles subjected
to a detailed diagnosis.
As the inspection process progresses from screening to detailed
component diagnosis, inspection equipment and labor skill become increas-
ingly important and costly. The probability of correct inspection diag-
nosis and maintenance repair improves, however, at the expense of higher
costs.
As the computer model is currently configured, it may be used to
evaluate and optimize procedures based upon the first two approaches
to state inspection shown in Figure 2-1.
Quantitative Inspection Criteria
Inspection procedures and criteria for passing or failing vehicles
will usually be different depending upon whether the public or private
sector performs the inspection because of the factors previously dis-
cussed. The model is specifically structured to evaluate procedures
based upon:
0 Direct measurements of engine parameters (adjustments or malfunctions)
using commercially available or more sophisticated garage type
equipment.
0 Inference of engine parameter maintenance states from indirect
measurements such as emission levels under differing engine loads.
Table 2-1 provides a summary of the maintenance options and the
emission species affected. The user selects those combinations he wishes
to investigate; the computer program may then be instructed to select
values of the pass/fail inspection criteria, either placed directly on
the engine parameter or on a screening variable, which optimizes the
14
-------
program figure of merit. Alternatively, if a more restrictive failure
criteria is desired to achieve larger emission reductions, the user may
directly input his own values of pass/fail criteria.
Maintenance Performed
The model user first specifies those engine parameters he wishes to
have maintained in a mandatory program. The choices will depend upon
the existing regional air quality and specifically upon those pollutant
species which constitute the greatest health and economic hazard (e.g.,
exceed the Air Quality Act Standards). For example, a region with a
chronic photochemical smog problem would preferentially desire reductions
in HC and NO , possibly constraining the reductions such that a specific
/\
HC/NO ratio is obtained. Maintaining parameters related to the induction
X
system in this case may actually be detrimental to the general air quality
since CO decreases at the expense of increased NO . The model user
X
should select those combinations of engine parameter maintenance options
which best satisfy his regional air quality needs. Table 2-1 also
provides general information with regard to the relative effectiveness of
maintaining specific engine parameters. An estimate of the effectiveness
of selective maintenance treatments can be obtained by algebraically summing
the appropriate emission index. For example, performing only a complete
induction system repair results in factors of + 2, +5, and -3 for HC, CO
and NO , respectively. This particular procedure would not be appropriate
X
in a region concerned with photochemical smog since HC is marginally
reduced at the expense of a nearly equal increase in NO .
X
15
-------
Table 2-1 Maintenance Options Available
within the Economic Effectiveness Model
Engine Parameter/System
Idle:
Fuel/air
RPM
Timing
Ignition:
Misfire
NOV Control
/\
Induction:
Air Pump
PCV
Air Cleaner
Vacuum Kick
Heat Riser
Maintenance
Treatment
set rich F/A to spec
set slow RPM to spec
set advance to spec
repair as required
repair as required
repair or replace
clean or replace
clean or replace
set rich to spec
free
+ Decrease in emission upon indicated maintenance
- Increase in emission upon indicated maintenance
Numeral indicates relative magnitude of change.
Relative Emission Changes
HC CO NO
+1
+1
+1
+3
+1
+1
+1
0
0
0
+2
+3
-1
_]
0
-1
+1
+1
+1
+1
+1
+5
0
0
+1
0
+1
-1
-1
-1
0
0
-3
16
-------
2.1.2 System Constraints
The development and implementation of mandatory program is constrained
by a variety of socio-economic and technical factors. These constraints
limit the performance and consequently the effectiveness of a given
program design. The major constraints presently incorporated in the
model are as follows:
Garage performance effectiveness
User inconvenience
t Emission inspection reliability
t Basic emission reduction goals
Although general in nature, these constraints affect the various strategies
in different ways. For example, the reliability of maintenance for the
idle parameters is much greater than for the replacement parameters.
Consequently, the overall performance of an idle program will be less
effected by this constraint than the more extensive maintenance treatments.
These constraints play a large role in shaping the optimal system
design. The constraints built into the present model are static in
nature. That is, they remain invariant over time. This assumption
results in a conservative estimate of both cost and performance for
the developed program. The introduction of technological forecasting
into the model would allow for the modification of these constants
as new techniques become available.
17
-------
2.2 SYSTEM DESIGN
The development of an inspection/maintenance system design represents
the other major problem in formulating an optimal program specification.
The essential design elements are as follows:
Frequency of Inspection/Maintenance
Total number of inspection lanes
Number of inspection stations
t Mobile or fixed sites
0 Vehicle throughput rates
t Information processing configuration
System manpower
Geographical distribution of.stations
t Inspection certification
Maintenance compliance
Each of these elements contributes in one way or another to the total
system design and layout. Under the present study ground rules, a design
specification is formulated only for the state lane system. It is assumed
that market forces will determine the availability and location of
franchised garage service. Determining the optimal inspection period and
number of lanes and sites can be accomplished directly with the model.
The key tradeoff in ascertaining the optimal frequency of inspection
involves both costs and emission reductions. Short periods of inspection
normally yield greater emission reductions at relatively high costs,
whereas longer inspection periods produce smaller overall emission
reductions at modest costs. Historically, our analysis has shown that
a twelve-month period between inspections yielded optimal performance.
This result appears consistent with current administrative practices.
The primary tradeoff in determining the number of lanes and sites is
basically one of convenience. This decision involves contrasting user
inconvenience costs with inspection station capital and labor costs.
Labor and capital costs are directly proportional to the number of
inspection lanes and sites, while user inconvenience costs vary inversely
with the number of sites.
18
-------
The other variables listed above are best addressed outside the model
The resultant costs from adopting a specific policy, however, can be
inputted directly into the model for comparative analysis. The major
cost impact from these variables involves the processing of basic
inspection/maintenance information. The relatively high costs for this
operation can be attributed to the large number of vehicles processed.
19
-------
3.0 ECONOMIC EFFECTIVENESS MODEL
This section presents a detailed discussion of the basic engineering,
economic and system principles used in developing the Economic Effective-
ness Model. These principles are embodied in a series of analytical for-
mulations. Each describes one phase of the total inspection/maintenance
process. The discussion also focuses on how these modules are integrated
together to form the Economic Effectiveness Model. Furthermore, the
decision criteria, i.e., figure of merit, used in selecting between various
strategies is examined along with other measures of system performance.
3.1 SYSTEM OVERVIEW
A program of vehicle inspection and maintenance involves a complex
set of interactions between many components. The several components
together with their interactive effects define the inspection/maintenance
system. The function of the Economic Effectiveness Model is to provide
mathematical descriptions of these components and their interactions
and to thus characterize the behavior of the inspection/maintenance
process.
Emissions phenomena are crucial components of the system description.
The model, therefore, incorporates analytical representations of vehicle
emissions. Costs of inspection/maintenance are the other major dimension
of the system. The model includes techniques to estimate all costs of
an inspection/maintenance program and to link these costs with vehicle
emission rates. In addition, the model embodies descriptions of the
basic system operations and their interrelationships with system compo-
nents, and an explicit decision criterion on which to distinguish
between program designs. The model performs a statistical analysis
on predicted emission reduction and develops a figure of merit
based on the statistically significant results. Also incorporated into
the model are specialized methods for performing certain data transforma-
tions, e.g., integration of emission time histories. Figure 3-1 shows a
schematic representation of the basic analytical structure used to
describe the process.
20
-------
S
o
ro
5 2.
33
-------
3.2 VEHICLE EMISSION MODELS
The core component of the Economic Effectiveness Model is the vehicle
exhaust emissions module. This module describes the process by which
vehicles are inspected and maintained, and predicts the resultant emission
reductions achieved by the maintenance treatment. This mo.del uses the
data developed from the Experimental Emission Test Program (Vol. IV) in
characterizing the basic relationships. A list of the major elements
comprising the model are given below:
t Inspection
0 Direct engine examination
0 Indirect exhaust emission measurement
t Maintenance
Deterioration
Emission mean values
t Parameter distributions
t Mode emission distributions
The following presents a discussion on the structure of each of these
submodels and how they are integrated together to yield the required
formulation.
The emission related calculation steps for both direct and indirect
strategies, are shown in Figure 3-2. Starting at some initial level E",
as determined by the experimental program, the vehicle population emission
levels deteriorate over time. At some predetermined interval, the vehicle
population undergoes an inspection which will result in a segment of the
population requiring maintenance. This in turn will yield an average
emission reduction for the total population (as depicted by the Sau-Tootn
Curve). The data sets used in characterizing this process is also depicted
in Figure 3-2. This process is repeated over the life of the inspection/
maintenance program.
22
-------
EMISSION DETERIORATION RATES COMPUTED
FROM PARAMETER DETERIORATION RATES
AND INFLUENCE COEFFICIENTS.
ro
co
O
i
i
LU
>
LU
_l
z
u
LU
CL.
l/l
AE =
a.e
3 P.
f.
i
AP R.
EMISSION REDUCTIONS COMPUTED AS
A FUNCTION OF INFLUENCE COEFFICIENTS,
GARAGE MAINTENANCE EFFECTIVENESS,
REJECTION FRACTIONS AND PARAMETER
ADJUSTMENT.
INITIAL VEHICLE EMISSION
LEVELS DERIVED FROM EXTENDED
PHASE I FLEET DETERIORATION
PROGRAM
INSPECTION PERIOD
TIME
FIGURE 3-2 BASIC COMPONENTS OF PROCESS
-------
The model has been subdivided into three control types and five power
trains to reflect the characteristics of specific vehicles. This
classification scheme permits the specification of different pass/fail
criteria for each control and power train-type. Because of the lack of
sufficient experimental data, the model dues not presently differentiate
between the various classes of power trains.
The model "bookkeeps" the emission levels for each type and com-
bines them to form aggregate levels for the entire population. The
composition of the aggregate fleet changes over time as new cars
are introduced into the population. Consequently, the importance of
the post 1970 fleet grows as time advances. Estimates of the vehicle
population mix are made using the Vehicle population Model (see Section
3.6).
3.2.1 Inspection Models
Inspection procedures for testing a vehicle's state involve the quanti-
tative measurement of either engine block components and/or exhaust mode
emissions. These parameters and modes are characterized using a set of
frequency distributions derived from the experimental test programs. This
model can presently accommodate up to ten engine parameters and six mode
emissions. A complete list of these elements is shown in Table 3-1. For
convenience and effectiveness, these parameter and modes have been grouped
into generic engine subsystems. This classification scheme is also shown
in Table 3-1.
24
-------
TABLE 3-1 PARAMETER/MODE CATEGORIES
Subsystem
Idle
I
0
Ignition
-------
X P(Xf) dX
AX. = ^ (3-2)
,, 3cr
/ PCX.) dx
c.p.
where:
AX. = average parameter adjustment for maintaining sub-set
of population
This gives average adjustment for these vehicles that were maintained.
The product of P(X^) and AX^ yields the average adjustment for the total
fleet. If the cutpoint equals the lower limit of the distribution, the
resultant AX^ becomes the mean value. Both of these variables are used in
estimating the emission reduction achieved by the maintenance program.
Applying the assumption of statistical independence between malfunctions,
i.e., P(X./1X.) = P(X ) P(X.)} the most probable total number of vehicles re-
' J ' J
jected by a given inspection policy is given by:
n
VR = EJJ PCX^] V (3-3)
where:
V = total vehicle population
VR = average vehicle population rejected
U = Union of vehicles rejected by inspection
These values are used in computing the cost for a specific program.
Evaluating the effectiveness of inspection based upon measuring
exhaust emission involves a further step. The inspection policy statement
now evolves around selecting the specific emission signatures for reliably
selecting those engine parameter malfunctions to be maintained. The
data synthesis leading to the selection of these inspection/maintenance
pairs is discussed in Volume IV- The vehicle fraction rejected by
the inspection using an emission measurement performed in an operating
mode will usually contain multiple parameter malfunctions:
26
-------
(V X2...X ) (3-4)
Jc.p.
where:
P(em) = set of vehicles with emissions e rejected
c.p. by cut point, c.p.
P(Xn) = set of engine parameters within P(e ) to
be maintained
The cutpoint on the distribution represents the emission value at
which vehicles will be rejected. Some of the vehicles which were rejected
by the emission inspection procedure are in the distribution which falls
to the left of the optimum parameter cutpoint signifying that repair of
these vehicles will not be cost-effective. These errors are termed
"commission" errors. The region outside of the parameter distribution
P(X ) but within P(X-) to the right of the cutpoint represent those
vehicles which have been permitted to pass the emission inspection but
have excessive parameter deviations from standard manufacture speci-
fication. These errors are called "omission" errors. Figure 3-3 shows the
relationship between these two types of errors.
The implication here is that an emission inspection does not uniquely
identify individual maladjustments but points to failures within subsystems
of related engine parameters. These families may usually be classified
into a specific subsystem, (e.g., induction or ignition). This is consistent
with the fact that the diagnostic modes were shown to point to more than
one out-of-specification parameter in the statistically designed experiments
(see Volume IV). The development of the relationship between emission
inspection signatures and the subsystem maladjustments diagnosed is also
presented in that volume and briefly described below.
The errors of commission are expressed explicitly in the model through
the use of an inspection efficiency data field. This data has been developed
from the engine parameter field survey data by applying the following pro-
cedure:
Inspection cutpoints are systematically placed upon emission
mode(s) known to have diagnostic content
27
-------
PASS/FAIL
MANUFACTURE'S
SPECIFICATION
TOLERANCE
CONCENTRATION UNITS
COMPONENT UNITS
FIGURE 3-3 RELATIONSHIP BETWEEN MODE EMISSION
AND ENGINE COMPONENT DISTRIBUTIONS
The vehicles so rejected are sorted from the data bank
t Statistical attributes for the appropriate malfunctions found
in the data set are developed.
The remaining elements of this process, e.g., maintenance and certification,
are identical to the direct inspection approach.
3.2.2 Deterioration of Parameters and Emission Modes
A large, captive fleet of in-use vehicles is being tested to develop
the data needed for estimating engine deterioration rates and their effects
on emissions. The prime variable is the rate of deterioration of engine
parameters from their maintained state. Average emission deterioration
rates are developed from two components - those that can be explained by the
ten parameters under study and all others (e.g., compression and main car-
buretor metering). Equation 3-5 presents the relationship used in estimating
the emission deterioration rates
AM
10
I
dPT
APi
(3-5)
28
-------
where:
Ae,
= 1972 mean emission change with mileage from engine
parameter deterioration experiment.
96.
~- = influence coefficient for j^n emission and i^-n
i parameter from orthogonal experiments.
9 Pi
-= average engine parameter change with mileage from
^M engine parameter deterioration experiments.
C- = emission change with mileage because of undefined
deterioration factors.
Both AP./AM and de./dP, as well as C. are developed from the experimental
I J J
program. Currently, a linear model is assumed since sufficient data are
not yet available for a more sophisticated approach. Rates are assumed
independent of inspection interval or degree of enforced maintenance, but
are dependent upon the general control system class, uncontrolled, controlled,
or NO controlled. Generally, the undefined component will become a larger
A
part of the total emission deterioration as the vintage of the vehicle
increases. The parameter distributions are inputted into the model and
manipulated in tabular hlstorgram form.
The same process is followed in developing the mode emission distri-
butions. The only difference involves substituting the mode emission
influence coefficients for the 1972 CVS mass influence coefficients.
The model accounts for six emission modes -- IDLE HC, CO, NO , loaded
A
HC, CO and NO . Currently, neither of the NOV emission modes are used
X A
to diagnose engine malfunctions.
3.2.3 Effectiveness of Maintenance
The effectiveness of maintenance in reducing emissions is estimated
from the data acquired in the orthogonal tests and the variables given in
Equations 3-1 and 3-2. These tests are statistically designed experiments,
wherein engine parameters shown to have a significant impact on emissions
were systematically malfunctioned. Response coefficients, changes in emis-
sions per unit change in parameter are derived from these data by applying
the condition of orthogonality. The orthogonal experiments resulted in
estimates for both the first order and second order influence coefficients,
29
-------
d 6-
i.e., vvr1 and aV iv . The second order, or interactive effects, reflect the
a A . OA "A
i i j
experimental fact that emission changes due to simultaneous adjustments of
two parameters are not necessarily predicted by the linear sum of the two
adjustments taken singularly. One parameter is said to have interacted with
the other in this instance.
Equation 3-6 presents the fundamental equation used in predicting the
emission reductions achieved from a given maintenance treatment. This is
the so-called "Gravitational Law" of vehicle inspection/maintenance.
ae
2
n de
_! Ri Rk AxiAxk^rk--fi
-------
is accounted for at the end of the deterioration interval. This, in
general, leads to a conservative estimate of the total emission reduc-
tion achieved by a specific program. This delay in the accounting pro-
cedures is consistent with the actual time required to process the total
vehicle fleet.
Figure 3-4 summarizes the maintenance and deterioration process for both
parameters and emissions. The process shown here starts with a mode emis-
sion inspection which in turn identifies a set of parameters to be maintained.
These parameter adjustments in turn affect the level and shape of both the
model and mass emission distributions. They also affect the level and shape
of their own distributions. Following maintenance, each parameter and mode
for both the accepted and rejected fleets deteriorate over time to some new
state. These states are then pooled to form an aggregate distribution for
the various parameters and modes. At that time, these variates are re-
inspected and the process is repeated throughout the program time horizon.
The technique for the engine parameter strategy is identical except that
the mode emission distributions are not analyzed.
3.2.4 Reliability of Maintenance
Controlled experiments have been conducted in which ten vehicles with
simulated malfunctions were submitted to approximately 45 service organi-
zations (service stations, independents and new car dealers) for diagnoses
and repair. The purpose of these experiments is to determine the reliability
and cost of repair for vehicles rejected by the two basic types of
inspection, direct engine parameter and emission signature. The post
maintenance inspection of vehicle engine parameter states comprise
the basic data set describing maintenance effectiveness. Distribution
functions developed from these data for those parameters tend toward log
normal or bi-modal shapes depending upon whether they are adjustments or
component repair, respectively. The bi-modal distribution results because
certain malfunctions (e.g., misfire) have not been diagnosed and, therefore,
go unrepaired. Both the maintained engine parameter distribution and its
geometric mean are used within the computer model to reflect that component
of the engine parameter variability resulting from maintenance and the
average emission reduction effected, respectively. The influence of over
repair is reflected as an actual incremental cost of unnecessary repair.
31
-------
MAINTENANCE TREATMENT
CO
ro
EMISSION DISTRIBUTION
CUTPOINT NEXT INSPECTION PERIOD
EMISSION DISTRIBUTION EMISSION DISTRIBUTION
DETERIORATE OVERTIME
I
PARAMETER DISTRIBUTION
PARAMETER DISTRIBUTION
EMISSION DISTRIBUTION
PARAMETER DISTRIBUTION
FIGURE 3-4 IMPACT OF MAINTENANCE AND DETERIORATION
-------
It is assumed that this repair, on an average, is ineffective in reducing
emissions. This assumption is a reasonable one with regard to the experi-
ment in that a substantial effort was made to assure that all other engine
parameters were at manufacturer's specification. In the field some over
repair (i.e., exhaust valve repair) may indeed result in emission reduction,
albeit at a significantly higher repair cost. This is not expected to in-
fluence the estimated program cost-effectiveness figure of merit, cost per
weighted emission reductions, although absolute values of cost and emission
reductions will be slightly under predicted. The reliability of repair is
assumed to be constant over each inspection interval. Presently no quanti-
tative data on how repair reliability might change with inspection interval
is available. The reliability of repair is specified in terms of an ef-
ficiency factor for each parameter maintained, e.g., the efficiency factor
for RPM is 85%. This factor states that on an average, RPM is set .85 of
the way to specification or 15% too slow. Equation 3-7 shows the method
used for estimating these efficiency factors.
AP. - AP-
_ _J i ,m ,, 7x
ei air <3-7)
where:
P. is the average value of parameter "i" relative to
1 3 Ml
specification achieved by maintenance.
3.2.5 Base Line Emission Prediction
The emission time histories predicted through application of a mandatory
maintenance treatment account for only that fraction of the vehicle popula-
tion which were judged inadequately maintained. The majority of vehicles
undergo routine maintenance which also influences the emission and engine
parameter time histories. This voluntary maintenance also reflects the
present state of vehicle emissions as, for example, measured in the California
and EPA vehicle emission surveillance programs. The actual effectiveness of
a voluntary program is characterized by several variables, e.g., frequency,
extent and reliability. The extent of this maintenance may be deduced
through a combination of the influence coefficient and emission and parameter
deterioration rates. The technique used in estimating the annual adjustments
33
-------
achieved by a voluntary program is depicted in equation 3-8.
AXB = (Ae - c) A"1 (3-8)
where:
AXg = parameter adjustment for voluntary program (vector)
Ae = total emission increase up to deterioration (vector)
c" = emission increase due to non-standard parameter (vector)
A = influence coefficient matrix for all emission species
Both the baseline fleet and those vehicles which passed the inspection
undergo the prescribed voluntary program. The actual amount of emission
reduction applied to the mandatory fleet is computed by Equation 3-9.
(3-9>
where:
= fraction of vehicles passing the i parameter
inspection
The baseline model also uses the influence coefficient and parameter deter-
ioration rates in predicting vehicle emission levels at various time points,
Integration of the difference between the mandatory and voluntary program
yields estimates on the reduction of that can be achieved through an
inspection/maintenance Program. These estimates are used in formulating
the various figures of merit.
The distribution of the inspected variables are also adjusted for
voluntary maintenance affects. This adjustment is performed by shifting
all of the distribution functions (emission and parameter) by the average
values affected by voluntary maintenance, AXg. The implied assumption
is that voluntary maintenance occurs randomly, all cells in the distri-
bution functions being equally affected by voluntary maintenance.
34
-------
3.3 ECONOMIC ANALYSIS MODEL
Design of optimal systems of vehicle inspection/maintenance involves
the complex interaction of engineering and economic factors. The purpose
of the economic analysis model is to translate a set of engineering and
operational design characteristics into an equivalent measure of system
costs. When combined with the analogous output from the emission models,
these cost figures can be employed to arrive at an overall evaluation of
the specific system being considered. Figure 3.1 has already shown the
basic interrelations between the economic and other factors characterizing
the inspection/maintenance process.
This characterization focuses directly on the cost effectiveness of
the inspection/maintenance program. It attempts to compare the achieve-
ment per unit cost for a specific program design with similar figures
from alternate programs. In this comparison, achievements and costs are
both narrowly defined to be consistent with both program perspective and
the realities of quantifiability. Specifically, achievements are measured
in equivalent tons of reduced emissions and costs are based upon tangible
use of resources. This approach is to be distinguished from a cost/
benefit analysis of the same problem. The latter is based upon a much
broader definition of both system costs (tangible and intangible) and
achievements (tangible and intangible). Due to limits on our ability
to quantify accurately elements of these broader definitions, a cost/
benefit analysis of inspection/maintenance programs would be much more
qualitative in nature. The narrower focus of cost effectiveness is more
consistent with both the goals and scope of the current study and is
therefore reflected in the economic model described below. It attempts
to address cost and achievement elements, which are realistically quanti-
fiable without implying that all such system elements are accounted for.
The latter would require subjective estimates and interpretation beyond
the scope of this effort and, indeed, beyond the current state-of-the-art.
35
-------
3.3.1 Outline of Economic Model
The economic analysis model is shown schematically in Figure 3-5. It
operates on basic system design data to generate, ultimately, estimates
of total annual system costs. The relevant costs here are the explicit
and implicit costs to implement the program. Explicit costs include
expenditures to construct facilities and to perform inspection/maintenance
operations. Implicit costs are less tangible and generally are not
expressed in monetary units. They include, for example, the time the
vehicle owner spends in inspection and maintenance related activities.
Station location and configuration design are determined by considering
both types of costs.
Inspection, maintenance and user-time costs comprise the main elements
of the economic analysis model. The model estimates capital and direct
operating costs for both the inspection and maintenance processes. Capital
costs considered are those for equipment, land and facilities. Operating
costs include utilities, labor, materials, spares, fringe benefits and
general administration. All capital costs are discounted over a specified
period and are added to the projected direct operating costs to obtain
total annual operating costs. Total program costs over the time period
considered are computed as the sum of these annual operating costs, dis-
counted to present value. These costs are quoted exclusive of the user
inconvenience costs which are included in the evaluation of alternative
inspection/maintenance processes.
3.3.2 Major Elements of the Model
It is useful to divide the basic components of the economic analysis
model for the test population into two groups: those that estimate direct
or explicit resource costs of the program and those that estimate indirect
or implicit resource costs.
Explicit Cost Components
Explicit costs are the common costs related to the real exchanges
of funds for materials, goods and services.
36
-------
Training)
>=<
Equipment
Capital
Costs
Operating
"Costs
Inconvenience
j Costs :
Amortization
Factor
FIGURE 3-5 COST ESTIMATOR MODULE
-------
Capital costs are a major form of explicit system costs. The costs
associated with capital investment requirements are a function of the
basic inspection/maintenance strategies. For the case of a franchised-
garage system, no direct capital investment will be accounted for in the
program. This assumption presupposes that franchised licenses will be
awarded only on condition of a satisfactorily equipped garage. The
state inspection/franchised-garage maintenance strategy does require a
capital investment for the inspection facilities. These costs will depend
on the size of the car population, the length of the inspection interval,
and specific instrumentation and equipment requirements. In the model,
it is assumed that all investments come onstream at time zero and that no
existing state facilities are employed. Separate investment calculations
are performed for the building, land and equipment requirements for each
state-lane station. These calculations involve a scaling operation based
upon unit inspection and unit maintenance facilities defined in the system
design.
The contributions of these capital investment costs to annual costs
as indirect operating costs are computed using the concept of a sinking
fund. For the case of the facility for a single inspection station, this
relation is:
SF = (1 -X) i (1 + i)n + . . x (3-10)
(1 + i)n
where: SF = Sinking fund factor
i = Rate of interest
n = Amortization period
X = Salvage fraction
This can be interpreted either as financing through bonds which are
payable in full upon maturity or through internal funds which must be
replaced in full at the end of a fixed period. Analogous calculations
occur for all other investment categories.
For each inspection interval, direct operating costs must be added
to the above indirect operating costs to obtain the total/system operating
costs. Under the direct category are separate calculations for wage
costs, administrative costs and miscellaneous operating costs for both
inspection and maintenance. In addition, a charge for labor and parts is
38
-------
incurred under the maintenance activity. Wage costs for a single station
are broken down into two portions: costs incurred at straight-time over
the normal working day and costs incurred at a specified overtime rate to
service the queue remaining at the end of the normal working day. Mis-
cellaneous operating costs reflect such items as electricity and certain
basic supplies.
Implicit Cost Components
The system costs discussed so far are only part of the total program
costs. We must add to these explicit costs an estimate of the implicit
cost represented by driver inconvenience. These implicit costs reflect
resource expenditures on the program that are not accompanied by a real
flow of funds.
The total time spent by users whose vehicle passed the inspection is
considerable, and it is reasonable to expect that, without an imposed
program, this resource would be employed in other pursuits from which
the individual would derive a benefit. The model, therefore, computes
a monetary estimate of these lost benefits which compose the value of
private time expended on the program. It does this by computing the
driving time to and from the station and waiting time at the station.
Waiting times at inspection station locations are defined from a queueing
model. This model assumes a Poisson distribution of vehicle arrival
times at the inspection station. Adding the traveling time and waiting
time to the actual vehicle inspection time yields the total inconvenience
time. For the case of the emission signature inspection, an added processing
time for some vehicles is incurred for reinspection. This additional
time is charged against the program if the failed vehicle passes its
second inspection. No user time charges are allocated for the corre-
sponding maintenance activities since they constitute the compliance
element of the program.
The conversion of these times to a direct dollar amount is done using
a social cost of $2.00/hour. Thus, a direct comparison can be made
between these costs and the designed facilities costs. The more stations
deployed in the system, the lower the social cost to the public and
39
-------
vice versa. One of the more essential dimensions of the system design
is the tradeoff to be made between explicit and implicit costs to obtain
the most cost-effective inspection/maintenance program.
Costs of the Base Population
All of the above costs refer to the resources necessary to implement
a given inspection/maintenance program. Under certain situations, the
relevant cost figure for evaluative purposes is the difference between
this system cost and that incurred under normal vehicle maintenance. As
shown in Figure 3-1, cost data for the base case can also be generated
by the economic analysis model. It is assumed that normal maintenance
occurs over periods identical to those imposed in the inspection/
maintenance program. Unit cost figures describing average maintenance
costs for the age and distribution of the base population are employed
together with average maintenance intervals to obtain an estimate against
which the inspection/maintenance program costs can be compared.
3.3.3 The Effect of Time on Costs
The phenomena - economic and emissions - that relate to an inspection/
maintenance program are basically dynamic in nature. Time enters as a
variable and all events take place over a specified time
span. TO neglect the effect of time is to neglect a crucial dimension
of the problem.
The economic analysis model includes explicit procedures to account
for time effects on system costs. These procedures can be broken down
into two categories - inflating and discounting costs.
Inflating Costs
A fundamental problem in measuring costs relates to the nature of the.
monetary unit. While it is essential to have a constant monetary unit
upon which to base cost calculations, in reality, this unit varies over
time. If we desire to compare costs with reference to the initial year
as a datum level, the program will compute all costs in constant dollar
figures (constant here implies the use of a monetary unit whose value in
each year is equal to that of the initial year). On the other hand, we
40
-------
may recognize the variation of prices over time and choose to base cost
calculations on current rather than constant cost concepts. While the
first approach is valid for comparing relative resource usage in various
years, the latter is valid for comparing out-of-pocket costs. For
comparison of current dollar costs, the program includes provisions for
inflating all costs at a constant annual rate. The results presented to
date, however, do not include the effects of inflation.
Discounting Costs
Examination of the impact of time on systems costs leads to a further
observation. Not only may prices rise in time but a dollar spent in
the future is not equivalent in value to a dollar spent today. Time
itself has value and this is a reflection of the availability of alterna-
tive productive uses of funds. Because of available mechanisms for
employing funds productively and, thus, earning an interest or profit,
it is not realistic to weigh a dollar cost incurred today on an equal
basis with a similar cost incurred at some future date. To compare
future costs with present costs, the former must be discounted to
present value by a discount rate related to the productivity of capital
or the going market rate of interest. Equation 3-11 gives the discount
rate expression used in the model.
- (3-,,,
where: .,
DRn = Discount factor for n period
i = Interest rate
n = Program period
All costs are therefore discounted at an assumed constant annual rate
to permit comparisons of system costs on the basis of present worth.
3.3.4 Other Economic Factors
Two additional economic factors have been incorporated into the
model in an attempt to account for costs associated with operationalizing
the system. The first one involves the so called "overcharge" phenomenon
41
-------
observed in the franchisee! garage experiment. The actual price charged
for both inspection and maintenance was, in a number of cases, several
times greater than the' predicted cost[2]. An estimate was made on the
average amount of overcharge for the three inspection/maintenance
strategies. These costs are now included as part of the program's
operating expense.
The cost associated with the training of inspection personnel
represents the second economic factor added to the model. These costs
account for the time required to train personnel to operate a statelane
inspection station. The planned training program consists of three
distinct phases:
Classroom lecture
t Laboratory demonstrations and equipment maintenance
On-the-job training
The cost per employee for the training program has been estimated
at $500.00. The model treats the total cost of training, i.e., cost
per employee times number of employees, as an initial investment. This
investment is amortized over the time horizon of the inspection/main-
tenance process, e.g., 5 years, and then included as part of the annual
program operating cost.
Another economic factor pertaining to the implications of vehicle
maintenance on fuel consumption has also been examined. The repair
or adjustment of ignition system components, specifically misfire, will
result in a favorable improvement in fuel economy. This situation can
be attributed to the decrease in unburned hydrocarbons achieved in
the combustion process. A preliminary analysis of potential fuel savings
yielded a rough estimate of approximately $1.00 per car per year for the
total population. This analysis was based on an average fuel cost
42
-------
of $300.00 per year and an average misfire rate of 0.0035 percent. While
."I !" ,* 1
the cost reduction appears significant vis-a-vis training cost and user
time cost, it has not been incorporated intorthe model. .This is because
of the uncertainty in the basic estimate and the fact that such savings
would be applicable to only one of the candidate strategies, i.e.,
ignition tune-up.
3.3.5 Total System Cost
In summary, once system investment costs have been computed, the
model evaluates the indirect and direct operating costs and the private
user costs for the inspection/maintenance process at each inspection
period. These costs are summed for a single interval, discounted by
factors appropriate to the end of that interval, and the summed overall
intervals to provide a measure of total program costs. This total cost
figure enters directly into the figure of merit calculation as depicted
in Figure 3-1. It is given by:
n
TAG = V" DF, AOC, (3-12)
where:
TAG - Total annularized cost
AOCi - Annual operating costs for i year
n - Number of years in program
DF. - Discount Factor
43
-------
3.4 OPERATIONS RESEARCH MODEL
That portion of the Economic Effectiveness Model concerned specifi-
cally with facility sizing and configuration is termed the operations research
model. It describes the interrelationships between the number of
stations, number of lanes per station, length of servicing queues,
and amount of user inconvenience time involved in the actual operation
of the inspection/maintenance program. Separate models of each related
activity and their interactions are specified analytically.
For a given number of servicing lanes in the total system and a
particular size of facility in terms of lanes per station, the model
determines the required number of sites. The number of sites combined
with the car population and inspection interval set the mean arrival
rate and this figure, together with the inspection time and the station
size, yields the facility utilization factor.
The mean length of the service queue, L, can be established by
assuming a Poisson arrival distribution:
L = (3-13)
S] (1-P)2
where:
PQ = the probability of the service queue being of zero length
X = mean arrival rate
M = service rate = inverse of inspection time, t.
S = number of lanes per station
P = utilization factor
The waiting time in the queue follows directly as:
t _L
w \ (3-14)
44
-------
Given a region of total area A, N sites and an average vehicle
speed of 9, the commuting time for the individual is estimated as:
r ,1/2
t = 2 ' L -* (3-15)
c 9
The total impact of system operations on user time is then simply:
Total inconvenience time = t- + t + t (3-16)
i w c
45
-------
3.5 STATISTICAL MODEL
The results derived from the Economic Effectiveness Model are
basically deterministic. That is, the predicted emission reductions
are computed utilizing fixed relationships for each operational step.
Obviously, a real program of vehicle inspection/maintenance involves
activities which cannot be characterized deterministically. For example,
consider the impact of maintenance effectiveness on overall program per-
formance. This uncertainty in inspection effectiveness is directly trans-
lated into uncertainties in predicted emission reductions. It becomes im-
portant, therefore, to ascertain the statistical significance of predicted
emissions reductions. The selection of an inspection procedure based on
the computed figure of merit may be inappropriate since the estimated em-
ission reductions may not be statistically significant.
To evaluate the implications of the program uncertainties, a statis-
tical inference model is incorporated within the Economic Effectiveness
Model. The function of this model is to:
t Test whether model predicted emission reductions are
statistically significant (i.e., greater than zero)
Estimate confidence limits on statistically significant
emission reductions
Estimate confidence limits on the emission time history
profiles.
The model utilizes the emission predictions for both the baseline and
test fleets to perform these various statistical tests.
Fundamentally, the statistical model is designed to generate the
variance for the distribution of emission reductions achieved by the
inspection/maintenance program. When combined with the mean values
generated by the emissions model, one can perform a formal statistical
test on the significance of reductions achieved under required inspection/
maintenance This general process is shown schematically in Figure 3-6.
46
-------
EMISSIONS
MODEL
EMPIRICAL
DISTRIBUTIONS
, TOTAL BASELINE
AND TEST FLEET
STATISTICAL i
MODEL
\ EMISSIONS
\
INSPECTION AND
MAINTENANCE
ERROR TERMS
STATISTICAL SIGNIFICANCE
OF EMISSION REDUCTIONS
FIGURE 3-6 ECONOMIC EFFECTIVENESS STATISTICAL MODEL
-------
There are four principal objectives associated with the cpnstruction
of the statistical model. The first is to determine the uncertainty
distribution of mass emissions for the test population and the base
population at several times during the process. The second objective
is to determine the uncertainty of the integral of the emission reduction,
i.e., total integrated tons, periodically and at the end of the process.
The third one is to determine the probability at each of these time
points that the mean emission difference is greater than or equal to
some specified constant. The final objective is to determine the
difference in the integral emission reductions which is significant to
the same confidence level at the end of the process.
There are two distinctly different approaches that can be taken to
test the significance of analytically estimated emission reductions.
Both are incorporated within the statistical model and can be employed
on an optional basis. The first utilizes empirically derived aggregate
distributions on HC, NO and CO obtained from the fleet experimental pro-
gram (Vol. IV). Variances obtained from these distributions are then used
to test the significance of model results. This method was the first
to be employed by virtue of data availability as established by the emission
test program. It is feasible, however, only for the extensive B or
major tune-up strategy.
The second approach utilizes an analytical procedure for estimating
variances on emission reductions. In this case, these variances are built
up from basic error information.
The main sources of uncertainty in predicting the performance of
candidate inspection/maintenance programs can be divided into two sets.
The first set consists of those uncertainties associated with the
inspection/maintenance process, namely:
Inspection measurement variance (i.e., instrumentation)
Maintenance reliability
The other set entails those uncertainties in the actual emissions
data base. These uncertainties are due to the fact that attributes of
48
-------
the total population have been estimated from relatively small samples.
In the case of influence coefficients derived from the orthogonal
experiments, the selected 11 cars were assumed to be characteristic of
the total population. The chief sources of uncertainty in the emissions
data base are:
Correlation of emissions-to-engine parameter variation
(i.e., residual error from orthogonal experiments)
Vehicle manufacturer-to-manufacturer emissions variability
Emissions variability caused by out-of-specification
engine parameters (a function of maintenance state).
The emission distributions for each specie are estimated during each
inspection/maintenance period using the distributions for the previous
period convoluted with the maintenance effects and associated error
terms. These distributions are then statistically compared with those
for the baseline fleet as in the alternate procedure.
The analytical procedure is obviously much more flexible. Unlike
the empirical approaches, it relies on fundamental error data which is
independent of inspection/maintenance strategy. It can, in principle,
be employed to assess the uncertainties associated with any inspection/
maintenance strategy.
The variances obtained by one of the above alternatives are then
combined with mean emission values estimated by the emissions model for
both baseline and test fleets to determine the statistical significance
of the estimated reductions (see Figure 3-1). The standard "t" score
statistical test is used in comparing these resultant test and base
distributions. The null hypothesis used to test whether the two samples
came from different populations, i.e., that the means are significantly
different, is:
HQ: UT = UB (3-17)
where: UT = test mean
UD = base mean
D
49
-------
The alternative hypothesis is:
If the analysis produces a positive test, the null hypothesis can be
rejected and that a difference in means does exist (accept H^).
Utilizing the computed statistic, we can also establish confidence limits
around the predicted emission reduction at each time point:
a^x^b (3-19)
where:
a = lower confidence limit
b = upper confidence limit
x = XB - XT
If two-sided 90% confidence limits are placed on the distribution, then
it can be stated that there is a 90% chance that the predicted emission
reductions will fall within these limits. If a one sided test becomes
desirable, it can be stated that there is a 90% chance that the emission
reductions will exceed the value a.
The figure of merit can now be recomputed using the statistically
significant emission reductions. Once this has been accomplished, the
various inspection/maintenance procedures can be reordered based on the
revised figure of merit. The reordered set can then be compared to the
initial set to determine whether the relative attractiveness of the
candidate procedures has been altered.
50
-------
3.6 UTILITY MODELS
The present Economic Effectiveness Model employs a wide variety of
utility routines and algorithms. These are used for performing the
quantitative calculations required to complete the analysis of a specific
inspection maintenance strategy. The two most salient routines consist
of an integration package and a probability function algorithm. The
integration routine (which employs an Euler method) computes the
total exhaust emissions by weight over the program's time horizon.
These results are utilized directly for developing the program's figure
of merit. The probability function algorithm provides estimates on vehicle
subsystem and population rejection fractions using the basic parameter
and/or mode emission distributions. This function is composed of Boolean
expressions for estimating both the union and intersection of selected
parameter and/or mode emission sets. These calculations are performed
based on the fundamental assumption that all parameters and all mode
emissions are independent. Empirical estimates have indicated that while
this is true for parameter distributions, such is not the case for the
mode emissions, especially the idle measurements. A control probability
component has been incorporated into the probability function to account
for the observed interdependence.
Another important routine in this group is the vehicle population
model. This model provides estimates on the attrition rates and new car
compositions for each year of the inspection/maintenance process. Tnis
model, in effect, removes most of the restrictive assumptions regarding
the size and characteristic of the vehicle population to be studied. The
model will simulate the quantitative change in population as more new cars
(post 1970) are introduced while pre-control (pre 1966) and control (1966-
1970) leave through natural attrition. The net result will be a consider-
able improvement in aggregate emission levels and therefore the validity
of inference drawn from estimated emission reductions. The demographic
data can be incorporated into the model for conducting comparative analysis.
In addition to the aforementioned models, a number of smaller routines
are utilized in the calculational process. They include:
51
-------
Linear interpolation algorithm
Two-dimensional emission time history plotter
Legendre polynomials curve fit
t Statistical routine for computing mean and standard
deviation of functional distributions.
The interpolation algorithm is used in developing the parameter and/or
mode emission frequency distributions for the next time point. The
analytically derived emission time histories are based on a Legendre
polynomial curve fit of the numerical data.
52
-------
3.7 DECISION CRITERION
Up to this point, we have described the manner in which the simulation
model computes measures of emission levels and relevant costs for a given
policy statement regarding vehicle inspection and maintenance. We need
now to identify an acceptable selection criterion which embraces with a
single value a measure of the goals of the program. Comparison of
different values of the figure of merit permits rapid assessment of
relative economic effectiveness of various policies. Ideally, then, we
would select that policy set (i.e., inspection interval, emission level,
pass/fail criteria, etc.) with the "best" figure of merit. Here, the
term "best" refers to the lowest value of the figure pf merit.
Unfortunately, no one figure of merit appears to include all of
the desired characteristics. The simulation model instead has the
capability of examining several different figures of merit, thus permitting
a determination of the sensitivity of the optimal decision to the chosen
objective function. The most relevant figure of merit can be expressed by:
Figure of Merit = PyamAEC°St (3-20)
J J
where:
W. = weighting function for each emission specie
AE. = emission difference between baseline and test program
J
This relationship provides a basis for comparing the voluntary and mandatory
programs with the cost of the mandatory program. The figure of
merit units are in discounted dollars per weighted tons of emission
reductions. Thus, program effectiveness can be read in terms of so
many dollars to achieve a reduction of one composite ton.
As can be seen, the weighting function establishes the degree to
which emission specie reductions impacts the program design. Having
fixed the weighting of emission reductions the model can determine the
optimal pass/fail criteria and system design for the several proposed
inspection/maintenance strategies. In actuality, the weighting of
emission reductions must reflect the air pollution problem of the various
53
-------
urban centers. Since some regions are more concerned with high ambient
CO levels than with HC levels, they would weigh CO reductions higher
than those of HC or NO.
The mechanism for actually determining the most attractive policy
set from among the several proposed inspection/maintenance approaches
should include not only the figure of merit, but also the inspection
costs per car and attendant emission reductions. These latter two
parameters are important in that they relate to the practical aspects
of emission control. For example, it could be assumed that a program
producing emission reductions less than 5%, no matter how economically
attractive, would not be very effective as a control scheme. The
guidelines selected for this study are in the form of the following
cost constraints and emission reductions goals:
t Average cost of six dollars per car for an idle program
was the maximum allowable
A program which provides emission reductions (HC and/or
CO) of less than 5% was unacceptable.
These guidelines, when used in conjunction with the figure of merit,
provide the criteria for analytically identifying the "best" inspection
procedure and system design.
Each combination of inspection procedure and system design can be
looked upon as a strategy. By examining the various strategies with
the economic effectiveness model, an ordinal ranking of these strategies
based on their figures of merit can be developed. It becomes fairly
straightforward to then identify the optimal strategy by merely selecting
the one which ranks first and conforms to the cost and actual emission
reductions guidelines described above.
54
-------
4.0 ANALYTIC METHODS OF SOLUTION
The above sections of this report have described the elements of
the mathematical model of an inspection and maintenance system. These
elements include both a data base which describes empirically the
magnitudes of system components and a methodology which integrates and
synthesizes the data into a coherent description of the system perfor-
mance. In this section, several uses of the model will be described.
Each of these uses or modes of operation provides a distinctly different
method for investigating the properties of a particular inspection/main-
tenance design and for drawing inferences regarding its attractiveness.
There are essentially three operational modes in which the model
can be employed:
1. Simulation
2. Optimization
3. Sensitivity Analysis
Each of these modes will be discussed in detail below.
4.1 SIMULATION
Simulation is conceptually the simplest mode in which the Economic
Effectiveness Model can be operated. It represents a first order attempt
to investigate the nature and interactions of a specific inspection/
maintenance program design.
To perform a simulation, one must assign explicit values to all
system independent variables. These are the strategic and tactical
variables available to the policy maker in designing an inspection/
maintenance program (e.g., inspection interval and number of lanes per
station). Given a complete definition of the policy to be examined,
the Economic Effectiveness Model will simulate the behavior of the
system in response to that policy. This simulation involves estimating
the dynamic character of the various phenomena of concern - costs
and emissions - and summarizing the overall results of the policy in
a figure of merit. Simulation is then a procedure for predicting the
impact of a given inspection/maintenance policy on the economics and
emissions behavior of the system.
55
-------
4.2 OPTIMIZATION
Optimization implies a step beyond pure simulation. It
attempts, to employ a series of simulations to identify the set of
values of system design variables that lead to the best system given a
specific decision criterion. The discussion of optimization which follows
is divided into two parts. First, the general methodology of optimiza-
tion is explained. Second, linear programming, a particular optimiza-
tion technique which is used to perform certain optimizations' of subsystem
variables, is described as it relates to the system model.
4.2.1 General Optimization Methodology
Values of system variables which optimize simple nonlinear or
complex linear mathematical models can often be found by means of
rigorous analytical techniques. Given, however, a complex nonlinear
system such as the inspection/maintenance model, rigorous procedures
are of little value. Resort must then be made to numerical heuristic
methods to obtain an approximate set of optimal system design variables.
This involves the use of a series of system simulations in sequence to
parametrically step towards the optimal system design. One of the de-
cision criteria described above is used to determine the optimal value
of a particular system design variable. In principle, the procedure
would proceed along these lines:
A. If there are n system design variables X. (i = 1, -, n),
conduct a series of simulations in which values of Xi vary
discretely over a relevant range while values of X. (i = 1>
... j-1, j + 1, ..., n) are held constant at predetermined
levels.
B. Given a decision criterion C = f(Xi Xn), identify the value
Xj* which maximizes (or minimizes depending on the nature of C)
the value of C.
C. Focusing now on \ (K * j), conduct a series of simulations
in which values of X|< are varied discretely over a relevant
range while values of~X-j (i = 1, j - 1, j + 1 -, K - 1,
K+ 1, "n,r\) are held constant at predetermined levels and
Xj = Xj*.
D. Given a decision criterion C, identify the value \, which
optimizes C.
E. Continue in this manner until optimal values of all system
design valuables have been identified.
56
-------
While the above parametric optimization procedure, in the limit, requires
considerable iteration to converge on an exact set of design values, it
leads quite rapidly to an approximate optimal set which is sufficiently
accurate for most purposes. This set, then represents the design of an
optimal inspection/maintenance system based on the selected figure of
merit and the particular system class being examined.
4.2.2 Linear Programming Algorithm
For large sets of independent variables, the above procedure would be
prohibitively expensive. To reduce analysis costs, and in recognition
of their varying impact on system design, an optimum set of engine
parameter or mode emissions pass/fail criteria is estimated via a linear
programming algorithm imbedded within the larger system model.
Linear programming offers a useful, approximate solution
to the problem of identifying optimal values for the above variables.
A computational sub-loop estimates locally optimal cut points by means
of the linear programming algorithm. The relationship between the
objective function of the linear program and its independent variables
X-j used in this application, i.e., engine parameter rejection rates
is given below.
1 a ?
where:
parameter setting
W. = relative weight assigned to j specie.
J
AX. = average parameter adjustment for failed vehicle
j_L_
R. = failure probability for i parameter
The objective function, Z, is the weighted reduction in emissions achieved
by maintenance and the problem is to identify specific values of R. which
maximize Z.
This maximization may be subject, however, to two basic classes of
inequality constraints:
57
= change in emission of j specie per unit change in i
-------
1. That the emission reduction for each specie exceeds a threshold
level
3e.
f 8pfAXiRi-^
where: b. = threshold reduction for jth specie
2. That the average cost per vehicle per inspection not exceed
a given value
? d,- R-i < g
i n ' ~
where: g = maximum allowable cost per car
d. = prorated cost per unit adjustment of the i
parameter
th
The b.'s are normally expressed in terms of some minimum percentage
J
emission reduction desired for each exhaust pollutant, e.g., 10% HC and
10% CO reduction. These values are exactly analogous to the emission
reduction program goals employed in earlier studies. The cost constraint
equation is used to relate the cost of adjusting or replacing engine
parameters with total system costs. The g coefficient represents an
assigned program cost for a given inspection/maintenance procedure that
cannot be exceeded.
The above linearized version of the pass/fail determination procedure
will yield estimates of the optimal rejection factors for each parameter.
These estimates can then be employed to develop values of the optimal cut
points of each parameter in the inspection process through an iterative
scheme.
This iterative scheme first computes for the rejected vehicle popula-
tion a set of mean value engine parameter settings. Using the basic engine
parameter distributions, a systematic search is made to find the pass/fail
criteria which will yield the optimal rejection fraction. In this manner,
then, a linear programming algorithm can provide an approximate mechanism
for determining pass/fail criteria for multi-parameter inspections. The
58
-------
same basic technique can also be used in deriving mode emission cut points
for the emission signature strategy.
This method of estimating optimal values of these design variables is
used only at the initiation of any particular simulation, although it could
be extended to each time point if system sensitivity warranted. In effect,
then, within each simulation is a sub-optimization of inspection pass/fail
criteria. Parametric optimization described above is necessary only to
determine optimal values of the remaining system design variables.
59
-------
4.3 SENSITIVITY ANALYSIS
Sensitivity analysis is in a sense a halfway house between simulation
and optimization. It involves more than merely estimating the impact of
a specific policy on a specific system, yet stops short of identifying
optimal values of system variables. Specifically, sensitivity analysis
utilizes a sequence of simulations to determine the sensitivity of key
analytical results to changes in a particular element of the system
model. These simulations involve analysis of policy designs and system
definitions that vary only in the value assigned to the particular element
being examined. In this manner, the impact of that element on system
behavior can be isolated through parameterization of the value of that
element, all other design and system values being held constant.
Sensitivity analysis can be performed to establish the effects on
procedure effectiveness and selection of:
1. Changes in assumptions or ground rules of the model
2. Changes in policy variables
3. Changes in empirical data employed in the model.
An important aspect of a sensitivity analysis involves defining a so-
called nominal or standard case. The impact of various changes in
system input on program performance is then measured relative to this
reference. The nominal case selected as a reference is typically an
idle parameter inspection/maintenance program for the Los Angeles basin.
If desired, assessment can also be made of the influence of system
variables on the performance of a program which involves more extensive
inspection and maintenance. Presented in Appendix A are several
examples of program assumptions which can be investigated using
sensitivity analysis.
60
-------
4.3.1 Model Structure
The model incorporates specific assumptions regarding the extent and
frequency of voluntary maintenance. These characteristics have direct
bearing on the predicted baseline emissions levels and therefore on
emission reductions predicted by the model. More frequent and/or more
extensive voluntary maintenance implies lower baseline emissions and
potentially lower reductions for a mandatory program. The reverse is
also true. By varying voluntary maintenance behavior, one can determine
the sensitivity of policy selection to assumptions made in this area.
Maintenance effectiveness assumptions are also built into the model.
Obviously, the degree of effectiveness of maintenance performed under the
inspection/maintenance program determines, to a major degree, the reductions
achieved under the program. Various assumptions can be made regarding
maintenance effectiveness and simulations can be performed to establish the
impact of maintenance variations on program success.
An important ground rule of the model involves the decision criterion.
Yet, it was stated earlier that no single criterion is perfectly acceptable.
It is crucial, then, to determine the sensitivity of program selection to
the particular criterion employed. This, too, can be established via a
series of simulations of the same group of policies but using different
decision criteria.
4.3.2 Program Variables
The length of the inspection interval is closely connected to both
system costs and emission reductions. The shorter the interval, the
greater the costs but also the higher the reduction in emissions. On the
other hand, the longer the interval, the lower the costs and reductions.
The establishment of the exact sensitivity of the figure of merit to
variation in inspection interval is crucial to understanding the nature of
the inspection/maintenance system and ultimately to identifying an optimal
design.
61
-------
This is also true for the number of lanes per station. More lanes
mean more capital investment but lower user inconvenience with the reverse
also true. Design of the most economically (i.e., socially acceptable)
effective inspection/maintenance program requires the estimation, therefore,
of the sensitivity of the figure of merit to variations in the number of
lanes per station.
4.3.3 Empirical Data
Parameter deterioration rates represent a key dimension of the empirical
description of the emissions phenomena in the model. They determine the
degree to which maintenance is required as well as the success of any
maintenance activity. Higher rates mean more frequent maintenance and
higher reductions. Analytical results must be examined over a realistic
range of deterioration rates to establish the related range of economic
effectiveness of an inspection maintenance policy.
The actual effective reduction of any program is computed as a weighted
average of the reductions in HC, CO and NO . These weighting factors, while
X
estimated empirically, still involve a subjective judgement of a number of
external factors. Because of the relationship between these weighting
factors and the figure of merit, program effectiveness is, in turn, a function
of the values of these factors. By parametrically varying these values,
one can determine the sensitivity of program selection to weighting factor
data employed.
4.3.4 Regional Evaluation
The above examples imply a micro sensitivity analysis, i.e., examination
of the relationship between procedure selection and variation in a particular
dimension of the model. Macro sensitivity analysis is also possible and
regional evaluation can be viewed as such a process. Here, the concern is
with the impact of changes in sets of components on the selection of the
best inspection/maintenance procedure. Each component set - weighting
factors, cost factors, population characteristics, - serves to define
a specific air quality region and to distinguish it from all others. By
changing these micro component sets, one can establish the macro sensitivity
of policy selection to regional variations.
62
-------
APPENDIX A
STUDY GROUND RULES AND ASSUMPTIONS
Presented herein is a summary of the study ground rules and assump-
tions expressed or implied in this report.
1) All mass and mode emission levels and reduction percentages
are reported in terms of an average value for the entire
vehicle population.
2) The effect of vehicles entering and leaving the population
because of attrition and new production are considered.
However, all new production vehicles are assumed to have
the same parameter, mass, and mode emission characteristics
as 1971, NO controlled vehicles.
X
3) Emission mean values for vehicle population treated by both
the engine parameter and emission inspection procedures vary
with time (deterioration) and with the extent of maintenance.
4) Basic maintenance of those normally adjusted engine parameters
not covered in the enforced maintenance procedure is assumed
to be performed voluntarily by the vehicle owner.
5) All mandatory maintenance is performed in franchised garages.
Mandatory maintenance is limited to restoring the engine
parameter listed in Table 2-1 to manufacturer's specification.
6) Inspection procedures requiring large capital expenditures
(i.e., the purchase of equipment for either remote sensing
or exhaust emission measurements) are always performed with-
in a state operated system.
63
-------
7) All vehicles failing a state inspection are reinspected by
the maintenance organization, only those engine parameters
actually failed are maintained.
8) Pass/fail inspection criteria are optimized for the first
inspection interval and remain invariant with time.
9) The basic cost of maintenance labor and parts is estimated
using Chilton's Labor Guide [2], The actual average invoice
cost is estimated by applying an overcharge factor repre-
senting unnecessary repair.
10) Estimated mean emissions reduction are based on measurements
made with the 1972 Federal Test Procedure.
11) The parameter deterioration rates and influence coefficients
are assumed to be invariate throughout the country. The
initial engine maintenance state ts determined by the Detroit
and Los Angeles parameter field evaluations.
12) User inconvenience costs are applied only to those vehicles
passing the initial inspection. The resulting maintenance
action is not assumed to be an inconvenience since it is in
compliance with the law.
13) The potential positive benefits of maintenance in terms of
improved fuel economy or operating reliability are not
reflected in the cost-effectiveness analysis.
14) After the first inspection interval (where major malfunctions
are repaired), engine parameter malfunctions are assumed to be
randomly distributed and therefore, statistically independent
of each other.
15) The effectiveness of voluntary maintenance is assumed
constant throughout the country.
16) The training costs incurred in setting up the initial state
lane program are incorporated into the program's figure-of-merit.
64
-------
17) Only those parameters which yield cost-effective results
are utilized in the specific application.
18) The effectiveness of repair is determined from data developed
in the garage survey experiment.
19) The parameter deterioration and influence coefficient for
all three control types is assumed to be linear and constant
for each inspection period.
20) Estimates for the statistically significant emission reduction
are made using the variance developed from the fleet deterior-
ation program.
21) All maintenance effects are applied at the end of the
inspection interval.
22) An estimate of the achieved reduction for the year is based
on one-half of the total reduced computed at the end.
23) Presently, no difference is made between the various vehicle
power trains.
24) The criteria for passing an inspection involves the state
of engine parameter and/or mode emissions and not composite
mass emission levels.
25) Vehicles failing a mandatory inspection program do so because
of lack of proper maintenance and not because of inspection
errors.
26) The basic costs for inspection/maintenance (e.g., hourly
rate and parts) are equal throughout the country.
65
-------
APPENDIX B
MODEL LIMITATIONS
The model, although general in design, does not account for several
factors which may influence the outcome of proposed or implemented strate-
gies. The two most significant factor are technological forecasting and
allocation of the cost burden. The model presently assumes that no signi-
ficant technological improvements will occur during the time horizon of the
program. The introduction of new control technology in the 1974-1975
period may significantly impact the emission reductions achieved from a
given strategy. As previously cited, the model assumes that all vehicles
entering the population are characterized by the same emission levels,
influence coefficients and deterioration rates than those developed for the
post 1970 fleet, i.e., 1971.
Another limitation closely related to this issue involves the uncer-
tainty in estimating the effect of major engine repair on predicted emission
reductions. The model computes the amount of emission reduction due to a
voluntary program using a fixed level of maintenance. A major tuneup during
the life of the program could dramatically alternate the basic state of the
vehicle population. The model is also limited in terms of the lack of
experimental data beyond 12,000 miles. This problem should improve, however,
as more time series experimental data become available.
66
-------
The question "Who should pay?" represents the other salient issue not
considered in the analysis. This particular facet of the program has been
omitted since it does not directly impact the effectiveness of candidate
procedures. Several options are available for cost sharing the operation
of a mandatory program of vehicle inspection/maintenance- They included:
User charge
DMV general fund
Vehicle manufacture warranty program
Federal revenue sharing.
Each of these alternatives goes beyond the problem of caoital investment
financing for a stateline system (see Section 3.3). The merits and dis-
advantages of each must be examined in detail before a specific approach
could be identified. Furthermore5 the selection of an optimal policy may
differ depending on the characteristics of the region under examination.
67
-------
APPENDIX C
INPUT/OUTPUT FEATURES OF THE ECONOMIC
EFFECTIVENESS COMPUTER MODEL
C.I INTRODUCTION
Presented herein is a descriptive narrative on the salient input/
output features of the Economic Effectiveness Computer Model. The model's
input/output system has been designed to accommodate a wide range of
inspection/maintenance options. Basically, the input options can be
partitioned into three categories -- inspection procedure, maintenance
treatment and geographical area.
The inspection procedure refers to the type and kind of diagnostic
evaluation undertaken prior to corrective maintenance. Presently, two
basic types of inspection strategies are available:
(1) Engine Parameter Inspection
(2) Exhaust Emission Inspection
Within each of these two approaches lies a number of different kinds of
inspection alternatives (e.g., idle). Based on a specific inspection
strategy, the model determines the optimum pass/fail criteria for the
various engine parameters and/or exhaust mode emissions.
Associated with each inspection alternative is a specific maintenance
treatment. Mandatory engine maintenance consists of adjusting, repairing
or replacing engine parameters which will yield the most cost effective
emission reductions for a given air quality region. The model assumes
68
-------
that all corrective maintenance takes place in a franchisee! garage and is
subject to existing maintenance reliability.
In addition to the various procedural options, the model requires
descriptive information on the demographic and air quality characteristics
of the candidate metropolitan area. The essential regional components
include: (1) vehicle population distributions, (2) vehicle emission levels
and engine state, and (3) a quantitative estimate on existing air quality.
The last one is used in developing the emission species weighting function.
The computer program which embodies the Economic Effectiveness Model
has been coded in FORTRAN IV and is currently operating on a CDC 6400-6500
computer system. Due to its design, it can process a number of
potential strategies with little or no change to the model framework or
data bank. Simplicity and flexibility characterize the salient features
of the input system.
69
-------
C.2 INPUT OPTIONS
Table C-l summarizes the current inspection/maintenance procedure
options in the Economic Effectiveness Computer Model. The model
partitions the engine block components into three major subsystems --
idle, ignition and induction. Associated with each subsystem and
inspection technique (either direct or indirect) is a specific maintenance
treatment. For example, the maintenance treatment for the idle subsystem
consists of adjusting idle air/fuel, rpm, and timing. The model permits
the combination of the various subsystems into more extensive inspection/
maintenance procedures. The two most logical extensions to the idle
program are:
(1) Idle adjustment with an ignition tuneup (Extensive A)
(2) Idle adjustment with an ignition and induction tuneup (Extensive B)
Both of these alternatives tend to yield greater emission reductions for
higher program costs. Obviously, other combinations of these subsystems
are also possible, however, past analysis has shown them to be less
attractive.
One of the key variables affecting the cost effectiveness of these
alternatives is the inspection pass/fail criteria. Two methods are
available for selecting values of inspection criteria for use in Economic
Effectiveness Model. One way involves the use of the model's linear
programming algorithm. Here, a set of optimal pass/fail criteria for
either the parameter and/or exhaust emission inspection are developed
for direct incorporation into the model. The other method consists of
prescribing a set of desired rejection rates over the time horizon of the
70
-------
TABLE C-l INSPECTION MAINTENANCE PROCEDURE OPTIONS
Engine Subsystem
Inspection Approach
Parameter Mode Emission*
Maintenance
Treatment
IDLE:
Fuel/Air
RPM
Timing
Idle CO
Tachometer
Timing Light
Idle CO
Idle HC
Idle HC
Set rich F/A to spec
Set slow RPM to spec
Set advance to spec
IGNITION:
Misfire
NOV Control
A
INDUCTION:
Air Pump
PCV
Air Cleaner
Vacuum Kick
Heat Riser
Idle HC/Cruise 45 HC Idle HC
Vacuum Gage (Dynamom-
eter)
Visual
Pressure Gage Cruise
Blockage Meter Cruise
Mechanical Gage
Visual
45
45
CO
CO
Replace plugs, points, & condenser
Repair or replace
Repair or replace
Clean or replace
Replace
Set rich to spec
Free
* Idle and Cruise 45 NOX emission measurements are also available.
-------
program. Given these values, the model will compute the corresponding
pass/fail criteria.
In addition to selecting the desired inspection/maintenance procedure,
the model also requires the identification of the candidate regional area.
Table C-2 presents the currently available regional options along with a
specification of the necessary regional input data. To date, detailed
vehicular demographic and emissions data has been collected for only Los
Angeles and Detroit. The data for the remaining areas is derived from
existing Los Angeles accounts. The singularly most important and con-
troversial regional input factor involves the emission species weighting
function. This function permits the combination of the three emission
species (HC, CO and NO ) into a composite numeration which can be used
X
directly in the program's figure of merit. Estimates of this function
are normally derived from existing regional air quality conditions.
The Economic Effectiveness Model can also be used to determine the
optimal design and configuration of .a state lane inspection system. Here,
the number and size of station sites can be traded off to ascertain the
optimal system mix. Table C-3 delineates the major operational and design
variables which not only influence the system configuration but also
overall program effectiveness. Nominally, the operational variables can
vary with time whereas the design variables, once they have been determined,
remain invariant. Inspection time and maintenance reliability have been
classified as operational variables since the ruling technology governing
their performance will be changing over the course of the program.
Table C-4 presents a schematic overview of the aforementioned input
options and data requirements utilized in the Economic Effectiveness Model.
72
-------
TABLE C-2 REGIONAL OPTIONS AND DATA REQUIREMENTS
GO
Metropolitan Areas
Los Angeles Basin
Denver
t Detroit
New York
Washington D.C.
Vehicular Attributes
Power Train and Population Distributions
Attrition and Growth Rates
Mass Emission Levels
Parameter and Mode Emission Distributions
Vehicle Control Types
Precontrolled
Controlled 1966-1970
t Controlled Post 1970
Air Quality Specifications
Emission Reduction Goals
Emission Species Weighting
Factors
-------
TABLE C-3 SYSTEM OPERATIONAL AND DESIGN VARIABLES
Operational Variables
Inspection Pass/Fail Criteria
t Engine Parameters
t Exhaust Mode Emissions
t Inspection Time
Maintenance Reliability
Design Variables
Program Horizon
Inspection Period
Inspection System Configuration
Inspection Equipment Specification
Information Processing System
t Inspection Training Procedures
t User Inconvenience
Program Financial Structure
-------
Table C-4 Flow Schematic of Input Options and Data Requirements
REGIONAL OPTIONS AND
CHARACTERIZATION DATA
t Metropolitan Area
Vehicle Attributes
Air Quality Conditions
cn
PROCEDURAL OPTIONS
Engine Parameter Inspection
Exhaust Emission Inspection
SYSTEM CONFIGURATION
SPECIFICATION
Operational Variables
Design Variables
PASS/FAIL INSPECTION
CRITERIA
Linear Programming
Vehicle Rejection Rates
ECONOMIC EFFECTIVENESS
MODEL
FOM =
$
-------
This input system, when combined with the model, constitutes the Economic
Effectiveness Computer Processor.
As an illustration of the input system, consider the data given in
Table C-5. For ease of implementation, the input system has been divided
into two components. The first one specifies, in a literal fashion, the
basic procedural options associated with the inspection/maintenance
process. For example, in executing an engine parameter extensive B
analysis the input system requires the following "key words": parameter,
idle, ignition, and induction. Input descriptors are also necessary in
identifying the candidate urban area and the composition of the vehicle
population to be used in the analysis. In this illustration, the input
includes all three control groups (uncontrol, control, and post 70).
In addition to these mnemonic descriptors, the input system also
contains a namelist routine. This routine permits one to input directly
values of selected operational variables. A partial listing of the name-
list variables is presented in Table C-5. Depending on the application,
the pass/fail critiera can be either inputted directly or computed from
the linear programming algorithm. The XCUT vector specifies the pass/
fail criteria for each of the ten parameters for each control fleet. The
SXCUT vector yields for each control fleet the pass/fail criteria for
the six mode emissions. The remaining namelist variables not listed
herein are primarily sensitivity variables. These include
the extent of voluntary maintenance and parameter deterioration rates.
Ordinarily, these internal variables do not change during the course of the
procedure evaluation.
76
-------
The bulk of the input data is normally invariant (e.g., influence
coefficients) and accordingly resides within the Economic Effectiveness
Model. This mechanism greatly simplifies the task of executing
multiple computer runs and minimizes potential sources of error. A
complete listing of all initial data is available through the use of
the DEBUG option. A discussion highlighting the relevant output
capabilities of the program is given in the following section.
77
-------
TABLE C-5 REQUIRED INPUT FOR AN ENGINE
PARAMETER EXTENSIVE B INSPECTION/
MAINTENANCE PROCEDURE
00
Input Descriptors
Parameter
Idle
Ignition
Induction
Loaded
LA
Uncontrol
Control
Post 70
Definition
Identifies engine parameter inspection
Identifies idle maintenance
Identifies ignition maintenance
Identifies induction maintenance
Misfire measured under load
Los Angeles Basin
Included Pre-1966 vehicles in population
Included 1966-1970 vehicles in population
Included post-1970 vehicles in population
Namelist Input
HORZN
LPICK
NPICK
SXCUT
TDIST
TINT
XCUT
NO
YES
Program duration
Linear programming option
Statistical analysis option
Mode emission pass/fail criteria (optional)
Parameter selection vector
Inspection interval
Parameter pass/fail criteria (optional)
-------
C.3 OUTPUT CAPABILITIES AND OPTIONS
The computer program has been designed to provide a wealth of informa-
tion on the emission reductions capability and associated costs of each
inspection/maintenance policy. Table C-6 exhibits a printout summary of
model generated data. This printout features several figure-of-merit esti-
mates, the computed emission reductions by species, and a variety of
accounting costs.
The program also generates the following ancillary information:
1) Mass emission time hfstories.
Aggregated
Control type
Power train
2) Vehicle population distributions and attrition rates over time.
3) Summary of input data.
4) Engine parameter and mode emission distribution plots and
statistics.
5) Pass/fail criteria and vehicle rejection probabilities by year.
6) Engine parameter rejection rates and average parameter
adjustments.
7) Summary of regional and operational design results.
8) Statistical confidence limits on predicted emission reductions.
A debug option has been incorporated into the major system routine
to assist in interpreting program output and in checking out new policy
alternatives. This option yields a complete diagnostic analysis on all funda-
mental calculations within the model.
79
-------
TABLE C-6 ECONOMIC EFFECTIVENESS SUMMARY PRINTOUT
*************
* TRW INSPECTION/MAINTENANCE *
* SYSTEM MODEL * ___ ____
********************************** " ~~ ..........
SUMMARY INFORMATION
ENCINE PARAMETER STRATEGY EXTENSIVE B
INSPECTION PERIOD IS 12.0 MONTHS
PAYOFF f UNCTION UNADJUSTED ( pCLLARS/hE IGHTED EMISSION) 2462.80
"PAYCFF" FUNCTION STATISTICALLY ADJUSTED (CCLLAVS/^EIGH"TED EMISSION) 14*6.52
PAYOFF FUNCTION AT END OF LAST YEAR i DOLL ARS /toE IGHTED EMISSICN) 8*52.65
hC EMISSION REDUCTION (PERCENT) JLL-H
"CO" EM I SSI tN REDUCTION"! PERCENT) 4.4C
KO EMISSION RECLCTICN (PERCENT) -.92
H? ^I^AGE EMISSIONS (TONS/CAY) 71^-81
CO" TVER AGE EMISSIONS t IONS/DAY)
NO AVERAGE EMISSIONS (TONS/DAY)
ft (COLLARS/YEAR) 12 5 11^2 42 :._75
~~' ~~
- . _
TOf AL COSTS" FOR~VGLUlifARY"MCGR"A«"~
-------
APPENDIX D
ANCILLARY MODEL DATA
The ancillary model data presented herein is incorporated in the
Economic Effectiveness Model. The data has been derived from sources
other than the experimental emission program. This data is used mainly
in characterizing the economical and operational elements of the model.
The data derived from the Emission Test Program is available in Volumes
IV, V, and VI.
The average annual parameter adjustments due to voluntary mainten-
ance are depicted in Table D-l. These voluntary maintenance adjustments
were formulated from the Air Resources Board surveillance data.
Tables D-2 and D-3 present inspection/maintenance and miscellaneous
costs used in the economic analysis model. The times and parts costs were
developed from both the experimental programs and Chi 1 ton's Labor Guide
[2]. As can be seen, the replacement parameters are the most costly and
consequently must yield larger emission reductions in order to be com-
petitive with the adjustment parameters, e.g., Idle RPM.
81
-------
TABLE D-l EFFECTIVENESS OF VOLUNTARY MAINTENANCE
AVERAGE
ANNUAL PARAMETER
ADJUSTMENTS DUE TO
VOLUNTARY MAINTENANCE
PARAMETER PRE-CONTRQLLED CONTROLLED POST 1970
Idle CO* 0.3 0.4 0.5
(± 1%)
Idle RPM* 25. 30. 35.
(+ 50 RPM)
Timing* 1.5 1.5 1.5
ra (+_ 2 degrees)
ro
Misfire 0.07 0.06 0.05
(Wires & Plugs)
NO Device
y\
Air Pump
PCV
Air Cleaner
Choke Vacuum Kick*
(+ 0.001 inches)
Choke Heat Riser 0. 0. 0.
*Parameter settings returned to manufacturers' specification
0.
0.
0.1
10.
0.
0.
0.
0.1
15.
0.
0.1
0.
0.1
20.
0.
-------
TABLE D-2 INSPECTION/MAINTENANCE COST COMPONENTS
00
co
ENGINE
PARAMETER
Idle CO
Idle RPM
Timing
Misfire
NO Control
A
Air Pump
PCV
Air Cleaner
Vacuum Choke Kick
Choke Heat Riser
EXHAUST MODE EMISSION (LANE
Idle HC
Idle CO
Idle HC + Cruise 45 HC
INSPECTION
TIMES
(Hours)
0.05
0.05
0.05
0.15
0.10
0.25
0.10
0.05
0.10
0.05
SYSTEM)
0.025
0.04
MAINTENANCE
TIMES
(Hours)
0.10
0.10
0.10
1.0
0.75
0.70
0.10
0.05
0.25
0.25
PARTS
($)
--
--
17.00
20.00
47.00
2.00
5.50
--
--
-------
TABLE D-3 MISCELLANEOUS DATA
CO
-pi
CONSTANT
Mechanics Hourly Rate
Station Attendant Hourly Rate
State Lane Overhead Rate
Information Processing Costs
Training Cost
Discount Rate
Inconvenience Hourly Rate
Average Equipment Costs
Station Size
Facilities Land Costs
Facilities Construction Costs
Emission Weighting Factors
(L.A. Basin)
HC
CO
NO
VALUE
$10.00/Hour
$ 3.50/Hour
50 Percent
$ 1.00/Car
$500/Man
7 %/Year
$ 2.00/ Hour
$20,000/Station
600 Sq, Ft.
$ 2.00/Sq. Ft.
$10.00/Sq. Ft.
0.6
0.1
0.3
-------
REFERENCES
1. "The Economic Effectiveness of Mandatory Engine Maintenance for
Reducing Vehicle Exhaust Emissions," Vol. Ill, "Procedures
Development," TRW Systems Report in Support of CRC APRAC Project
No. CAPE-13-68, 1971.
2. Chilton's Labor Guide and Parts Manual, Motor Age, 40th Edition,
1969.
85
------- |