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

• Published in: Axioms Vol. 12; no. 11; p. 1054
• Main Authors: Elbatal, Ibrahim, Hassan, Amal S., Diab, L. S., Ben Ghorbal, Anis, Elgarhy, Mohammed, El-Saeed, Ahmed R.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.11.2023
• Subjects: Bayesian estimation; binomial distribution; Burr distributions; Censoring (Statistics); Engineering; Estimates; Failure; Independent variables; Insulation; Life expectancy; Maximum likelihood estimators; Medicine; Metropolis–Hastings algorithm; Monte Carlo simulation; Parameters; Random variables; Reliability analysis; Strains and stresses; Strength of materials; Stress relaxation (Materials); Stress relieving (Materials); stress–strength model; Type-II progressive censoring; Saudi Arabia
• ISSN: 2075-1680; 2075-1680
• DOI: 10.3390/axioms12111054

In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, 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=PW<V 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.