Inference for a Step-Stress Model With Type-II and Progressive Type-II Censoring and Lognormally Distributed Lifetimes

TL;DR

This paper develops maximum likelihood estimation methods for a step-stress life test model with lognormal lifetimes under various censoring schemes, providing bias, error analysis, and confidence intervals through simulation.

Contribution

It introduces a novel approach to estimate parameters in a complex step-stress model with censored data and lognormal distribution, including iterative solutions and confidence interval evaluation.

Findings

MLEs are derived and their properties analyzed.

Bias and mean square error of estimates are evaluated.

Confidence intervals are assessed via Monte Carlo simulation.

Abstract

Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows testing the products at higher than usual stress conditions to induce failures more quickly and economically than under typical conditions. A special case of ALT are step-stress tests that allow experimenter to increase the stress levels at fixed times. This paper deals with the multiple step step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-II and Progressive Type-II censoring. For this model, the maximum likelihood estimates (MLE) of its parameters, as well as the corresponding observed Fisher Information Matrix (FI), are derived. The likelihood equations do not lead to closed-form expressions for the MLE, and they need to be solved by means of an iterative procedure, such as the Newton-Raphson method. We then evaluate the bias and mean square error of the estimates and provide asymptotic and bootstrap confidence intervals. Finally, in order to asses the performance of the confidence intervals, a Monte Carlo simulation study is conducted.