Fuzzy analysis for steady-state availability: a mathematical programming approach

Abstract

Steady-state availability has been widely applied as a measure to evaluate the reliability characteristics of a repairable system. However, it is generally not realistic to make assumptions concerning failure time and repair time distributions. Thus, this article has developed a procedure to construct the membership function for fuzzy steady-state availability. Based on Zadeh’s extension principle, a pair of mathematical programs is formulated to find α-cuts of fuzzy steady-state availability. An explicit closed-form expression for the membership function is derived by taking the inverse function of the $\alpha$-cut. To illustrate the interpretation and practical value of fuzzy availability in real-world applications, several numerical examples are provided and discussed.