Fuzzy vs. Traditional Reliability Model for Inverse Weibull Distribution

Abstract

In this paper, fuzzy stress strengths RF=P(Y≺X) and traditional stress strengths R=P(YX) are considered and compared when X and Y are independently inverse Weibull random variables. When axiomatic fuzzy set theory is taken into account in the stress–strength inference, it enables the generation of more precise studies on the underlying systems. We discuss estimating both conventional and fuzzy models of stress strength utilizing a maximum product of spacing, maximum likelihood, and Bayesian approaches. Simulations based on the Markov Chain Monte Carlo method are used to produce various estimators of conventional and fuzzy dependability of stress strength for the inverse Weibull model. To generate both conventional and fuzzy models of dependability, we use the Metropolis–Hastings method while performing Bayesian estimation. In conclusion, we will examine a scenario taken from actual life and apply a real-world data application to validate the accuracy of the provided estimators.

Keywords

• fuzzy set
• inverse Wibull distribution
• stress–strength reliability
• Metropolis–Hastings algorithm
• maximum likelihood
• maximum product of spacing