Simulation Techniques for Strength Component Partially Accelerated to Analyze Stress–Strength Model

Abstract

Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of δ=P(Y<X) were proposed when the strength variable was subjected to the step–stress partially accelerated life test. The point estimators computed were maximum likelihood and Bayesian under various symmetric and asymmetric loss functions. The interval estimations constructed were approximate, bootstrap-P, and bootstrap-T confidence intervals, and a Bayesian credible interval. A Markov Chain Monte Carlo approach using Gibbs sampling was designed to derive the Bayesian estimate of δ. Based on the mean square error, bias, confidence interval length, and coverage probability, the results of the numerical analysis of the performance of the maximum likelihood and Bayesian estimates using Monte Carlo simulations were quite satisfactory. To support the theoretical component, an empirical investigation based on two actual data sets was carried out.

Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution

“…The iteration procedure will stop when |σ (k) − σ (k+1) | is small enough. Substituting σ into (10), we can have α1 and α2 . Accordingly, the ML estimator of R is…”

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“…It is also increasingly used to estimate the probability that one variable exceeds another [5,6], which is of great significance in practical application and has been widely used in various fields, such as electrical cable failure analysis, leukemia treatment, and jute fiber testing. See more details for [5,[7][8][9][10].…”

Based Copula Reliability Estimation with Stress-Strength Model for Bivariate Stress under Progressive Type II Censoring

“…de la Cruz et al [12] discussed the reliability issues of single-component stress-strength models when stress and strength follow independent unit-half-normal distribution models, using both maximum likelihood estimation and bootstrap techniques to construct confidence intervals of model parameters. Recently, Yousef et al [13] obtained various point and interval estimators based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions when the strength variable was subjected to the step-stress partially accelerated life test.…”