Reliability inference for multi-component stress-strength systems with heterogeneous Lomax-distributed components under progressive censoring

Abstract

Abstract In this paper, the m-component stress-strength parameter is considered under progressive first failure (PFF) censoring scheme, assuming the stress and strength variables follow the Lomax distribution. To achieve this, various classical and Bayesian estimation methods are explored under two scenarios. In the first scenario, where the common parameters of the stress and strength variables are unknown, maximum likelihood estimation (MLE), Bayesian estimation using the Markov Chain Monte Carlo (MCMC) method, asymptotic confidence intervals, and highest posterior density (HPD) credible intervals are derived. In the second scenario, where the common parameters of the stress and strength variables are known, MLE, Bayesian estimation using the MCMC method and Lindley’s approximation, the uniformly minimum variance unbiased estimator (UMVUE), as well as the asymptotic confidence intervals and the HPD credible intervals, are derived. A Monte Carlo simulation study is conducted to evaluate and compare the performance of the proposed methods. Additionally, two real datasets are analyzed for illustrative purposes.

Keywords

• Multi-component stress-strength parameter
• Progressive first failure censoring
• Lomax distribution
• MCMC method
• Simulation
• Lindley’s approximation