Optimum step-stress partially accelerated life tests for the truncated logistic distribution with censoring

This paper deals with the optimal designing of step-stress partially accelerated life tests (PALTs) in which items are run at both accelerated and use conditions under censoring. It is assumed that the lifetime of the items follow truncated logistic distribution truncated at point zero. Truncated distributions arise when sample selection is not possible in some sub-region of the sample space. The logistic distribution is considered inappropriate for modeling lifetime data because left hand side of its distribution extends to negative infinity, and this could conceivably result in modeling negative times-to-failure. This has necessitated the use of truncated logistic distribution truncated at point zero for modeling lifetime data. Unlike the widely studied exponential, Weibull and lognormal life distributions, the failure rate of truncated logistic distribution is increasing and more realistically bounded below and above by non-zero finite quantity. The optimal change-time for the step PALT is determined by minimizing either the generalized asymptotic variance of maximum likelihood estimates (MLEs) of the acceleration factor and the hazard rate at use condition or the asymptotic variance of MLE of the acceleration factor. Inferential procedure involving model parameters and acceleration factor are studied. Sensitivity analysis is also performed.