Bayesian system reliability assessment under the vague environment

Abstract

Classical reliability assessment is based largely on precise information. In practice, however, some information about an underlying system might be imprecise and represented in the form of vague quantities. Thus, it is necessary to generalize the classical methods to vague environments for studying and analyzing the systems of interests. On the other hand, Bayesian approaches have shown to be useful when there is some prior information about the underlying model. In this paper, Bayesian system reliability assessment is investigated in vague environments. To employ the Bayesian approach, model parameters are assumed to be vague random variables with vague prior distributions. This approach will be used to create the vague Bayes estimate of system reliability by introducing and applying a theorem called “Resolution Identity” for vague sets. We also investigate a computational procedure to evaluate the vague Bayes estimate of system reliability. For this purpose, the original problem is transformed into a nonlinear programming problem which is then divided up into eight subproblems to simplify computations. Finally, the results obtained for the subproblems can be used to determine the membership functions of the vague Bayes estimate of system reliability. Two practical examples are provided to clarify the proposed approach.