Modeling Uncertain Bayesian System Reliability Analysis

Abstract

Classical system reliability analysis is based largely on crisp (also called “precise”) lifetime data. However, in practical applications, due to the lack, inaccuracy, and fluctuation of collected data, such information are often imprecise and expressed in the form of fuzzy quantities. Therefore, it is necessary to reformulate the conventional methods to imprecise environments for studying and analyzing the systems of interests. On the other hand, Bayesian approaches have shown to be useful for small data samples, especially when there is some prior information about the underlying model. Most reported studies in this area deal with obtaining the $\alpha $ -cuts of system reliability estimator which given a lower and upper bound for system reliability. This article, however, proposes a new method for Bayesian estimation of system reliability based on $\alpha $ -pessimistic approach. To do this, we use the definition of $\alpha $ -pessimistic and existing prior information about the unknown parameter under investigation. Moreover, to employ the Bayesian approach, model parameters are assumed to be fuzzy random variables with fuzzy prior distributions. Two practical examples are provided to clarify the proposed method.

Keywords

• Bayes estimator
• loss function
• Mellin transform
• membership degree
• system reliability
• fuzzy random variable