Optimum Multi-Objective Ramp-Stress Accelerated Life Test with Stress Upper Bound for Burr Type-XII Distribution

This paper deals with the formulation of optimum multi-objective ramp-stress accelerated life test (ALT) plans with stress upper bounds for the Burr type-XII distribution under type-I censoring. It is impractical to estimate only one objective parameter after conducting such costly ALT tests. Therefore, an optimum ramp-stress ALT plan with multiple estimating objectives has been designed. The Burr type-XII life distribution has been found appropriate in accelerated life testing models. The commonly used Weibull and exponential distributions are its limiting cases, and the log-logistic distribution is its particular case. The inverse power law, and a cumulative exposure model are assumed. The optimal test plan consists of determining the ramp rate by minimizing the weighted sum of the asymptotic variances of the maximum likelihood estimator of quantile lifetimes at design constant stress. The method developed has been illustrated using an example, and the effects of the pre estimates of design parameters were investigated. Comparative study has also been done to highlight the merits of the proposed model.

Acronyms ALT

accelerated life test

Asvar

asymptotic variance

cdf

cumulative distribution function

pdf

probability density function

ML

maximum likelihood