Statistical inference for Gumbel Type-II distribution under simple step-stress life test using Type-II censoring

TL;DR

This paper develops statistical inference methods for the Gumbel Type-II distribution in simple step-stress life testing with Type-II censored data, including MLE, Bayesian estimators, and optimal censoring plans, validated through simulations and real data.

Contribution

It introduces new estimation techniques and optimality criteria for Gumbel Type-II distribution under step-stress testing with censored data, combining MLE, Bayesian, and simulation approaches.

Findings

MLE and Bayesian estimators perform well in finite samples.

Optimal censoring plans improve estimation accuracy.

Methods are validated with real data analysis.

Abstract

In this paper, we focus on the parametric inference based on the Tampered Random Variable (TRV) model for simple step-stress life testing (SSLT) using Type-II censored data. The baseline lifetime of the experimental units, under normal stress conditions, follows the Gumbel Type-II distribution with $\alpha$ and $\lambda$ being the shape and scale parameters, respectively. Maximum likelihood estimator (MLE) and Bayes estimator of the model parameters are derived based on Type-II censored samples. We obtain asymptotic intervals of the unknown parameters using the observed Fisher information matrix. Bayes estimators are obtained using Markov Chain Monte Carlo (MCMC) method under squared error loss and LINEX loss functions. We also construct highest posterior density (HPD) intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Three different optimality criteria have been considered to determine the optimal censoring plans. Finally, the methods are illustrated with the analysis of two real data sets.