Optimum multi-objective modified constant-stress accelerated life test plan for the Burr type-XII distribution with type-I censoring

Accelerated life test is usually performed using constant, step, progressive, cyclic and random stress loadings. In most of the existing accelerated life test plans, the stress level changes instantaneously, which is impractical. So, it is desirable to increase the stress at some finite rate, since a sudden jump in stress level may cause a thermal shock or undesirable failure modes that may not occur at the normal use condition. To overcome this problem, modified constant-stress loading and modified step-stress loading have been used in the literature in each of which stress is increased from a low stress level to higher stress level at a finite rate. This article deals with the design of an optimum multi-objective modified constant-stress accelerated life test plan for Burr type-XII distribution with type-I censoring. The inverse power law and a cumulative exposure model are assumed. The optimal test plan consists of determining an optimum low stress level, and also optimum proportion of units to be allocated at low and high stress levels by minimizing the weighted sum of the asymptotic variances of the maximum likelihood estimator of quantile lifetimes at design constant stress. The multi-objective modified constant-stress accelerated life test plan devised has been explained using a numerical example and the effects of the deviations from the pre-estimates of the design parameters investigated. The proposed model has been compared with the pre-existing model using the simulated failure time data set. For the same data set the proposed multi-objective plan has been compared with a single-objective plan with respect to changes in the values of the parameters, equal weights and unequal weights.