Fuzzy reliability estimation using Bayesian approach

The Bayesian reliability estimation under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed to be fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of reliability by invoking the well-known theorem called ‘Resolution Identity’ in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.