Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution

Abstract

Mazucheli et al. introduced a new transformed model referred as the unit-Weibull (UW) distribution with uni- and anti-unimodal, decreasing and increasing shaped density along with bathtub shaped, constant and non-decreasing hazard rates. Here we consider inference upon stress and strength reliability using different statistical procedures. Under the framework that stress–strength components follow UW distributions with a known shape, we first estimate multicomponent system reliability by using four different frequentist methods. Besides, asymptotic confidence intervals (CIs) and two bootstrap CIs are obtained. Inference results for the reliability are further derived from Bayesian context when shape parameter is known or unknown. Unbiased estimation has also been considered when common shape is known. Numerical comparisons are presented using Monte Carlo simulations and in consequence, an illustrative discussion is provided. Two numerical examples are also presented in support of this study. Significant conclusion: We have investigated inference upon a stress–strength parameter for UW distribution. The four frequentist methods of estimation along with Bayesian procedures have been used to estimate the system reliability with common parameter being known or unknown.

Keywords

• bayesian point and interval procedures
• least square estimator
• stress–strength reliability
• maximum product of spacing estimator