Inference for Simple Step-Stress Model from Log-normal Distribution Under Type-I Censoring

Abstract

<p>It is well known that the accelerated lift-testing (ALT), which involves analyzing times-to-failure data of a product (system or component), is one of the testing procedures for traditional lifetime data. The ALT allows the experimenter to obtain the failure data at high stresses more quickly than under normal operating conditions. In this project, we apply a simple step-stress model (a special class of ALT) to a life-testing experiment when the times-to-failure data are assumed to be log-normal distributed under Type-I censoring mechanism. The objective of the project is to discuss inferential methods for the unknown parameters of the model by using the maximum likelihood estimation method along with the cumulative exposure model. Some numerical methods (such as, Newton-Raphson and quasi-Newton methods) for solving the corresponding nonlinear equations are discussed. Methods of constructing confidence intervals for the unknown parameters discussed here are those based on (i) asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study as well as a simulated data are used to verify the performance of these methods of inference.</p>