Expectation Analysis of the Probability of Failure for Water Supply Pipes

Abstract

The probabilities of failure for cast iron (CI), ductile iron (DI), polyvinyl chloride (PVC), and concrete cylinder (CC) pipes were analyzed to determine the pipe type that failed most consistently at the Honolulu Board of Water Supply (HBWS). In understanding the process of the probability of failure over time, expected failure rates were calculated. A pipe type with a low and consistent probability of pipe failure was preferred for asset management over one that displayed a high and volatile probability of failure. The probability of failure was derived from the failure rate, assuming a Poisson distribution. The data for each pipe type was analyzed and compared by using control charts, operating characteristic (OC) curves, and process capability indexes. The results of the control charts showed that CC pipes were the most stable. According to the OC curves, in which the hypothesis created was that the probability of failure was less than the upper specification limit, CI pipes had the highest probability of accepting the hypothesis when true. PVC pipes showed a low probability of accepting the hypothesis within the specification limits, but also a low probability of false acceptance of the hypothesis. Finally, process capability analysis found that CI and PVC pipes were able to meet their desired failure specification limits. Overall results are mixed—CI pipes performed the best according to OC curves and process capability analysis; PVC pipes were seen as the worst through the use of control charts and OC curves; CC pipes were the most stable according to control charts, but the worst in process capability. A rank order structuring of failure expectations concluded that CI pipes were the best, whereas PVC pipes were the worst. However, this finding does not translate into recommendations for pipe design. It was observed that actual failure rates and expectation analysis are distinct aspects; the expected performance of a pipe is independent of its actual performance.