Statistical Inference for a Simple Step-Stress Model Based on Censored Data from the Kumaraswamy Weibull Distribution

The step-stress accelerated life tests allow increasing the stress levels on test units at fixed time during the experiment. In this paper, accelerated life tests are considered when lifetime of a product follows a Kumaraswamy Weibull distribution. The shape parameter is assumed to be a log linear function of the stress and a cumulative exposure model holds. Based on Type II and Type I censoring, the maximum likelihood estimates are obtained for the unknown parameters. The reliability and hazard rate functions are estimated at usual conditions of stress. In addition, confidence intervals of the estimators are constructed. Optimum test plans are obtained to minimize the generalized asymptotic variance of the maximum likelihood estimators. Monte Carlo simulation is carried out to investigate the precision of the maximum likelihood estimates. An application using real data is used to indicate the properties of the maximum likelihood estimators.