Adaptive Hybrid Progressive Censoring in m-Component Reliability Model and Generalized Inverse Weibull Distribution

Abstract

In thispaper, the authors investigate the Bayesian inference of the m-component stress-strength parameter for the generalized inverse Weibull distribution under an adaptive hybrid progressive censoring scheme. The study considers three cases. In the first step, the paper employs the MCMC method to derive a Bayesian estimate of the m-component stress-strength parameter when both the common parameters for strengths and stress variables are unknown. Secondly, assuming that the common parameters are known, two approximation methods are employed: namely, the MCMC method and Lindley’s approximation. Finally, in a broader scenario where all parameters are distinct and undisclosed, the paper employs MCMC simulation to calculate a Bayesian estimate of the m-component stress-strength parameter. To evaluate and compare these methods’ performance, one Monte Carlo simulation is conducted.
Additionally, a real data set is used to implement theoretical methods proposed in this study.

Keywords: m-component stress-strength reliability; Lindley’s approximation; MCMC method; Adaptive hybrid progressive censoring
scheme.

2010 Mathematics Subject Classification. 62N05; 62F15