United States
Environmental Protection
Agency
Water Engineering
Research Laboratory
Cincinnati OH 45268
Research and Development
EPA/600/S5-87/003 Jan. 1988
<>EfiA Project Summary
Statistical Models for Water
Main Failures
D. H. Marks, S. Andreou, L. Jeffrey, C. Park, and A. Zaslavsky
/»
A detailed statistical analysis of pipe
break records from the New Haven,
Connecticut, and Cincinnati, Ohio,
water distribution systems focused on
deriving predictive models for pipe
failure probabilities at the individual pipe
level.
The statistical methodology of the
proportional hazards model was applied
to estimate failure probabilities in the
earlier phases of pipe deterioration.
Another set of models, derived for pipes
with frequent multiple breaks, assumed
a roughly constant break rate for the
later breaks.
These methodologies were useful in
statistically describing the failure pro-
cess and in distinguishing those pipes
most likely to break. The models pro-
vided insights into factors contributing
to breaks, such as pressure, land
development, soil corrosivity, and the
age of the pipe. Changes in data collec-
tion and coding are suggested that could
make possible improved models.
Water utilities can use this detailed
modeling of the probabilities of pipe
maintenance events over time in formu-
lating improved strategies for repair,
replacement, and rehabilitation.
This Project Summary was developed
by EPA'g Water Engineering Research
Laboratory, Cincinnati, Ohio, to an-
nounce key findings of the research
profect that It fully documented In a
separate report of the same title (see
Project Report ordering Information at
back).
Introduction
Mature water distribution systems are
currently facing problems commonly
associated with a deteriorating infrastruc-
ture. A majority of the systems in the
eastern United States have reached a
critical stage as reflected by high breakage
rates, loss of carrying capacity, and high
unaccountable water losses.
The premise of this report is that to
make the best use of the limited resources
available for maintenance, management
officials need current information reflect-
ing the relative degeneration of each
pipe, its importance within the distribution
network, and the economics of the main-
tenance alternatives. With this informa-
tion, management could systematically
determine the pipes and areas having the
highest priority for attention and imple-
ment improved strategies for replacement,
repair, and rehabilitation.
The models described in this report will
predict the probability of experiencing a
break in each pipe based on the historical
data on the system.
In addition to the immediate policy
recommendations flowing from predictive
aspects of the models, the models also
have an explanatory aspect. In the process
of developing the model, variables associ-
ated with increased probabilities of pipe
failure are identified. This information
gives insight into the mechanisms of
failure in the system.
The Cox proportional hazards model
was the primary statistical method used
for modelling pipe failure events. In
applying this model, failure events could
be defined as individual breaks, reaching
a certain number of breaks, or beginning
a run of consecutive breaks.
Because of the large number of pipes
with many breaks (more than 3 and as
many as 35) in the Cincinnati data set, it
was necessary to develop a model for
events in pipes that broke many times
during the period under study. This model
would be useful for estimating the long-
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term costs of maintaining the pipe and
comparing them with the cost of replacing
it.
It was found that there did not appear
to be a trend toward an increasing or
decreasing time between breaks after
the fourth break. A model was developed
to describe the break rate of a pipe from a
given starting point (either three or six
previous breaks), assuming that breaks
occurred at a constant rate at this stage.
Conclusions and
Recommendations
1. Break rates (frequency of pipe events
requiring a repair) varied greatly between
the Cincinnati and New Haven systems
and among different mains of a single
system. The methods used in this report
were able to model a substantial part of
the variability in breaking rates among
pipes. The proportional hazards model
was used successfully to model the first
three breaks; another model was used
to model breaks after the third break.
2. Two distinct failure patterns were
identified in large pipes (8 inches or
larger): slow breaks, with infrequent
breaks occurring at a rate increasing with
time, and fast breaks, with frequent
breaks (probability of failure of 50% per
year or more) at a roughly constant rate.
Proportional hazards regression can be
used to predict the hazard rate for breaks
while in the slow-breaking state, as well
as the probability of entering the fast-
breaking state. This methodology appears
to be applicable even when records of
breaks before a certain date for older
pipes are unavailable. Another model,
assuming a rate of breaking that was
roughly constant over time, described
much of the variability in breaking rates
among pipes that were in a fast-breaking
state after already breaking three or more
times.
3. The models help in understanding the
factors associated with breaks and make
possible the estimation of the probabilities
of future breaks. The following indepen-
dent variables affected the break rate:
internal pressure, time taken to second
break, number of previous breaks, period
of installation, pipe length, land develop-
ment over the pipe, and (in the Cincinnati
system) soil corrosivity.
High internal pressure is associated
with accelerated breaking in certain sub-
sets of the pipes. Land development over
the pipe may be a surrogate for external
loads transmitted to the pipe. Complex
patterns were found relating specific types
of land development to pipe breaks.
If the second or third break takes place
quickly, this appears to point to defects in
the pipe material or construction, or to a
high concentration of break-causing
factors that may be expected to accelerate
future breaks.
For the first few breaks, each successive
break tends to take place faster than the
one before. However, once a pipe has
had several breaks and is in a fast-
breaking state, successive breaks do not
accelerate although pipes that have had
many breaks are on the average in worse
condition than those with fewer breaks.
Pipe length has been used as a covari-
ate in the regression models. Omitting
this variable in previous studies implicitly
assumes that break-causing factors are
uniformly distributed along the pipe
length, so breaks are proportional to
length. In fact, the probability of failure
varied approximately with the square root
of length.
Young pipes (installed in the 1950's
and 1960's) were less reliable than older
pipes. This suggests that changes in pipe
and joint materials and construction
methods have had some detrimental ef-
fects, and use of these new materials
and methods should be reconsidered.
Pipes were found to be negatively af-
fected by high soil corrosivity only in the
Cincinnati system. This suggests a higher
overall level of corrosivity in the Cincinnati
pipes, which may be responsible in part
for the greater number of breaks observed
there.
4. Pipes tend either to break very quickly
(within about 5 years after the last break)
or to last 20 or more years without breaks.
Pipes having defects or stresses that make
a break likely will usually break within a
short time.
5. Ring cracks and holes appeared mainly
in the smaller pipes (under 12 inches),
with ring cracks being most frequent in
the winter months. Joint cracks and leaks
appeared in all pipe sizes and in all
seasons.
6. Failure probabilities and break rates
predicted by the models can be used
directly for assessing the reliability of a
water distribution system and of individual
pipes within a system. Repair, replace-
ment, and rehabilitation strategies for
deteriorating pipes are clearly affected by
the findings of this research. Several
rules of thumb that are currently popular,
such as replacement based solely on age
or the number of previous breaks, appear
to be inadequate. The pipes most likely to
break can be better distinguished using
models that include other factors as well.
7. "Left-censored" records that go back
only to a certain year can still be the
basis of a valid statistical analysis. Even if
pipe records have not been maintained
for this type of analysis, it would be
worthwhile to a utility to begin to keep
such records or to reconstruct them from
existing records.
8. More precise and useful results may
be obtained in return for a modest invest-
ment in improved data collection and
coding methods. The variables in the
existing New Haven and Cincinnati data
sets, including length, diameter, pressure,
date of installation, material, soil cor-
rosivity, land development, and the date
of each break were found to be useful in
the analysis. If pipe segments were coded
to have a more nearly uniform length, a
better model could be developed based
on these same variables. Additional in-
formation that would be useful in building
improved models would be the type of
break, exact location, and cause where
known; the method of repair used; and
years in which there were major changes
in pressure or new land development
over the pipe. Although not all of this
information could be conveniently coded
in a computerized data set, it would be
informative to examine the detailed re-
cords on break location and method of
repair for pipes with many breaks.
9. The models derived for the New Haven
and Cincinnati systems have enough in
common that some of their conclusions
could be applied to other cities as well.
Generally, however, it would be advisable
to begin building a data base for each city
in which these methods were being
applied, using a minimum of 20 years of
records.
10. Further research could test the gen-
eral usefulness of these methods by
applying them to the water distribution
system of other cities, particularly to
model break rates in a city in a dry region.
The full report was submitted in ful-
fillment of Cooperative Agreement CR
810558 by the Massachusetts Institute
of Technology, under the sponsorship of
the U.S. Environmental Protection
Agency.
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D. H. Marks, S. Andreou, L. Jeffrey, C. Park, and A. Zaslavsky are with the
Massachusetts Institute of Technology, Cambridge, MA 02139.
Jeffrey Adams is the EPA Project Officer (see below).
The complete report, entitled "Statistical Models for Water Main Failures,"
(Order No. PB 88-103 775/AS; Cost: $18.95, subject to change) will be
available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Water Engineering Research Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
U.3.OrFlGlALM/
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
EPA/600/S5-87/003
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