Inference in Simple Step-Stress Accelerated Life Tests for Type-II Censoring Lomax Data

Abstract

In this paper, step-stress accelerated life test is considered to obtain the failure time data of highly reliable units in specified conditions. It is assumed that the lifetime data of such units follow Lomax distribution with a scale parameter depends on the stress level and the shape parameter remains constant. It is also assumed that failure times occur according to a cumulative exposure model (CEM). Using this model, the maximum likelihood estimators (MLEs) and the respective confidence intervals (CIs) based on the asymptotic normality theory as well as the ones based on parametric bootstrap method are considered. In the context of prediction, point and interval predictions are also addressed. A simulation study has been performed to assess the estimation and prediction methods and a real dataset is analyzed for illustrative purposes.

Keywords

• Confidence and prediction intervals
• Conditional median predictor
• Cumulative exposure model
• Highest conditional density
• Lomax distribution
• Maximum likelihood estimation