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

Abstract

a b s t r a c tThis 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.

Local linear smoothing to estimate accelerated lifetime model with censoring and truncation

“…The results from the test are displayed in Table A. 4. If the p-value reported by the Schoenfeld residual test is below a significant level 0.05, we conclude that PH assumption does not hold.…”

“…Consequently, specific models and statistical procedures to analyze failure times data have been developed in the specialized literature. The proportional hazards (PH ) model (Cox [1]) and the accelerated failure time (AFT ) model (Lawless [2] and Nelson [3]) are frequently used in applied studies (see for example Srivastava and Mittal [4], Leea et al [5] and Ismail [6]). …”

On designing step-stress partially accelerated life tests under failure-censoring scheme

“…18 This article is organized as follows: In 'Model and test method' the assumed distribution and the test method are described. 'MLE of the parameters' considers the maximum likelihood estimates of the model parameters.…”

Bound lengths for Burr-XII distribution under step-stress PALT

“…In Step-Stress PALT, a test item is run first at normal use condition and, if it does not fail, then it is run at accelerated condition until failure occurs or the observation is censored. Several references have with SS-PALT, a little few of them are [13], [14], [15], [16], [17], [18] and [19].…”