Stress–Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal

Abstract

In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PWV, where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of δ=PWV for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of δ is derived. The Bayes estimator of δ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.

Keywords

• stress–strength model
• Burr distributions
• Type-II progressive censoring
• binomial distribution
• Bayesian estimation
• Metropolis–Hastings algorithm