Fuzzy Bayesian system reliability assessment based on prior two-parameter exponential distribution under different loss functions

SUMMARY The fuzzy Bayesian system reliability assessment based on prior two‐parameter exponential distribution under squared error symmetric loss function and precautionary asymmetric loss function is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. Because the goal of the paper is to obtain fuzzy Bayes point estimators of system reliability assessment, prior distributions of location‐scale family has been changed to scale family with change variable. On the other hand, also the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability have been provided. In order to achieve this purpose, we transform the original problem into a non‐linear programming problem. This non‐linear programming problem is then divided into four sub‐problems for the purpose of simplifying computation. Finally, the sub‐problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO. Copyright © 2010 John Wiley & Sons, Ltd. The fuzzy Bayesian system reliability assessment based on prior two‐parameter exponential distribution under squared error symmetric loss function and precautionary asymmetric loss function is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. Because the goal of the paper is to obtain fuzzy Bayes point estimators of system reliability assessment, prior distributions of location‐scale family have been changed to scale family with change variable. On the other hand, the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability have also been provided. In order to achieve this purpose, we transform the original problem into a non‐linear programming problem. This non‐linear programming problem is then divided into four sub‐problems for the purpose of simplifying computation. Finally, the sub‐problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO. Copyright © 2010 John Wiley & Sons, Ltd.