Bayesian system reliability and availability analysis under the vague environment based on Exponential distribution

Reliability modeling is the most important discipline of reliable engineering. The main purpose of this paper is to provide a methodology for discussing the vague environment. Actually we discuss on Bayesian system reliability and availability analysis on the vague environment based on Exponential distribution under squared error symmetric and precautionary asymmetric loss functions. In order to apply 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 and availability by introducing and applying a theorem called “Resolution Identity” for vague sets. 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. Finally, the sub problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.