Page 101 - Reliability and Maintainability of In service Pipelines

90 Reliability and Maintainability of In-Service Pipelines

The effect of randomness of variables on the probability of failure can be mea-
sured by an omission sensitivity factor. According to Ditlevsen and Madsen
(1996), the omission sensitivity factor with respect to random variable u i can be
determined by:

βðtÞj 1 2 α i u i =βðtÞ
ζ tðÞ 5 U itðÞ5u i 5 ð3:11Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
u i p 1 2 α 2
βðtÞ
i
where α is the normal unit vector to the limit state surface gðU; tÞ at checking
point u and time t (Melchers, 1999). As can be seen the omission sensitivity fac-

tor measures the relative error in the value of reliability index β if an input ran-
dom variable is replaced by a fixed value (i.e., treated as a deterministic variable).
Thus when the relative error of random variables (i.e., omission sensitivity factor)
is around one (ζ 1Þ, it may be appropriate to treat them as deterministic vari-
u i
ables if the full statistical information of them is not available.

3.6 Background and Methods for Reliability
Analysis of Pipes

Since large investment is required for building new pipeline networks for different
purposes such as urban water supply and/or energy infrastructure, it is unlikely to
replace the existing pipeline networks completely over a short period of time.
Therefore, the resort has to be maintenance and rehabilitation of existing pipelines.
To have an optimum strategy for maintenance and rehabilitation plans in the man-
agement of a pipeline asset, accurate prediction of the service life of in-service
pipelines is essential. But this cannot be achieved without an accurate method for
reliability analysis in which the likelihood of pipeline failure is determined.
Reliability analysis can cover a wide domain of failure assessment of struc-
tures and infrastructure including both service life prediction and failure rate pre-
diction. It should be noted that there is a clear distinction between the two terms:
Failure rate prediction of pipes: When the result of reliability analysis and/or
failure assessment is presented as a number of failures within a period of time
(e.g., breaks/year), it should be ideally considered as failure rate prediction.
Service life prediction of pipes: When in a study, service life of pipe(s), in
terms of time, is investigated; the study should be named as service life
prediction.

As a comparison, there is considerably less literature in the field of service
life prediction compared to the failure rate prediction of pipes. It needs to be clar-
ified that the focus of this book is on service life prediction of pipelines. To that