Theoretical and Conceptual Framework - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 16

environmental effects of a failure are minimal. Secondly, storage tanks usually available
within the network will keep a buffer volume for emergency situations. And thirdly, networks
typically contain redundancy and flexibilities planned in their layout.

Many repairable systems, including pipes, typically have a 'bathtub' shaped intensity
function. This is shown in Figure 2.3, where λ(t) indicates the failure rate (adapted from
Neubeck, 2004).

0.007

Early
failures

Chance and
wearout failures

0.006

Chance failures

Burn-in
period

Useful life period Deterioration

period

0.005

0.004

0.003

0.002

0.001

0

1 5 9 13 17 21 25 29 33 37 41 45 49

Pipe age (years)

Figure 2.3 Pipe failure rate as a function of age (adapted from Neubeck, 2004)

Immediately after a pipe has been laid and put into operation, the failure rate can be high and
because of poor transportation, stacking or workmanship during the installation. After early
faults have settled down, the intensity of bursts will be decreasing and remain relatively
constant for long periods of the pipe useful life. Following this period, the pipe starts
deteriorating faster, and the intensity of bursts will increase again. These bursts are
considered as wear-out failures.

Two approaches have been suggested in the literature to model the failure life time
distribution: (1) Homogeneous Poisson Process (HPP) and (2) Non-homogeneous Poisson
Process (NHPP). The HPP model neglects the time component of the failure and as such is
mostly appropriate for renewable systems where repairs are executed regularly and the age of
pipe is within the useful life period. According to Shinistane et al. (2002), the probability of a
pipe failure using the Poisson probability distribution is:

− β

p j = 1 − e

j

, where 2.6

β = λ

j j j

Exponent β j is the expected number of failures per year for pipe j , and λ j and L j its failure rate
and length, respectively. Goulter and Coals (1986) and Su et al. (1987) also used similar
methods with the HPP model to determine the probability of failure of individual pipes.
On the other hand, the NHPP model considers the time component and is therefore suitable
for the burn-in- and deterioration period during which the times between the failures are
neither independent nor identically distributed. The NHPP model also assumes negligible
repair times, meaning that the repair time will have no effect on the increase of the pipe