Water Resources Research Report



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Large and complex engineering systems are subject to wide range of possible future loads and conditions. Uncertainty associated with the quantification of these potential conditions is imposing a great challenge to systems‘ design, planning and management. Therefore, the assurance of satisfactory and reliable system performance cannot be simply achieved.

Water supply systems, as typical example of these engineering systems, include collections of different types of facilities. These facilities are connected in complicated networks that extend over and serve broad geographical regions. As a result, water supply systems are at risk of temporary disruption in service due to natural hazards or anthropogenic causes, whether unintentional (operational errors and mistakes) or intentional (terrorist act).

Quantification of risk is a pivotal step in the engineering risk and reliability analysis. In this analysis, uncertainty is measured using different system performance indices and figures of merit to evaluate its consequences for the safety of engineering systems.

The probabilistic reliability analysis has been extensively used to deal with the problem of uncertainty in many engineering systems. However, application of probabilistic reliability analysis is invariably affected by the well-known engineering problem of data insufficiency. Bayesian approach and subjective probability estimation are used to evaluate, express, and communicate uncertainty that stems from lack of information or data unavailability. They introduce a formal procedure for incorporating subjective belief and engineering understanding together with the available data.

Fuzzy set theory, on the other hand, was developed to try to capture people judgmental believes, or as mentioned before, the uncertainty that is caused by the lack of knowledge. Fuzzy set theory and fuzzy logic contributed successfully to the technological development in different application in real-world problems of different kinds, (Zimmermann, 1996).

This study explores the utility of the fuzzy set theory in the field of engineering system reliability analysis. Three new fuzzy reliability measures are suggested: (i) reliability index, (ii) robustness index, and (iii) resiliency index. These measures are evaluated, together with fuzzy reliability measure developed by Shrestha and Duckstein (1998), using two simple hypothetical cases. The new suggested indices are proven to be able to handle different fuzzy representations. In addition, these reliability measures comply with the conceptual approach of the fuzzy sets.

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Department of Civil and Environmental Engineering, The University of Western Ontario


London, Ontario, Canada


Civil and Environmental Engineering


Report no.: 045

New Fuzzy Performance Indices for Reliability Analysis of Water Supply Systems