OPTIMUM MULTI-LEVEL RAMP-STRESS ALT PLAN WITH MULTIPLE-OBJECTIVES FOR BURR TYPE-XII DISTRIBUTION UNDER TYPE-I CENSORING

Abstract

This paper considers optimal design for ramp-stress accelerated life test (ALT) with multiple stresses and multiple estimating objectives using Burr type-XII life distribution and 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 formulated. The need to analyze an ALT data with different life distribution models such as exponential, normal, Weibull, log logistic, etc., is necessitated since the use of correct life distribution model especially in the presence of a limited source of data-as typically occurs with modern devices, having high reliability, helps in preventing the choice of unnecessary and expensive planned replacements. The Burr type-XII distribution has a nonmonotone hazard function, which can accommodate many shapes of hazard function. The commonly used Weibull and exponential distributions are its limiting cases and log logistic distribution is its particular case. The distribution has been found appropriate for modeling failures that occur with less frequency and also when there is high occurrence of early failures. The inverse power law and a cumulative exposure model are assumed. The optimal test plan chooses the stress rates and proportion of units allocated to each stress 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, sensitivity analysis carried out and comparative study has also been done to highlight the merits of the proposed model.