Optimum Time-Censored Modified Ramp-Stress ALT for the Burr Type XII Distribution with Warranty: A Goal Programming Approach

Abstract

Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components. Much of the previous work on ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations. In the literature ramp-stress ALTs that have been formulated can be conducted when more than one test chambers are available; installation of which may prove to be costly. Even when one test chamber is used the stress rate remains constant throughout the duration of the experiment. It is not only necessary but imperative to examine if the test specimen is able to withstand differing stress conditions with the passage of time. This paper therefore, presents an optimal design of multi-objective modified ramp-stress ALT model with weighted goal programming approach. The modified ramp-stress uses one test chamber in place of the various chambers used in simple ramp-stress ALT thus saving experimental cost. With the market being increasingly competitive the emphasis today is on goal attainment with minimum deviations. Goal programming is a method to solve multi-objective problems that has applications in varied fields of engineering and operational research. The optimal plan consists in finding out relevant experimental variables, namely, stress rate, stress rate change point and warranty period, by using goal programming on weighted sum of variance of reliability function and expected warranty cost with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out. Comparative study has also been done to highlight the merits of the proposed model.