On the estimation of fuzzy stress–strength reliability parameter

Abstract

In this paper, we introduce a novel, more interpretative, membership function that can be used for the definition of fuzzy stress–strength reliability parameter R of a two-component system. We find the MLEs and UMVUEs point estimators of R, as well as the asymptotic and bootstrap interval estimators. In the wide empirical study for the case when both components are exponentially distributed, we examine the properties of introduced estimators. We also explore the impact of the membership function on the quality of estimators.