Robust Design of Accelerated Life Testing and Reliability Optimization: Response Surface Methodology Approach

Abstract

Due to cost and time savings and improving reliability, accelerated life tests are commonly used; in which some external stresses are conducted on items at higher levels than normal. Estimation and optimization of the reliability measure in the presence of several controllable and uncontrollable factors becomes more difficult especially when the stresses interact. The main idea of this chapter is employing different phases of response surface methodology to obtain a robust design of accelerated life testing. Since uncontrollable variables are an important part of accelerated life tests, stochastic covariates are involved in the model. By doing so, a precise estimation of reliability measure can be obtained. Considering the covariates as well as response surface methodology simultaneously are not addressed in the literature of accelerated life test. This methodology can be used on the conditions that a broad spectrum of variables is involved in the accelerated life test and the failed units have a massive cost for producers. Though considering covariates in the experiments, the optimization of reliability can generate more realistic results in comparison with noncovariates model. For the first step of this study, experimental points using D-optimal approach are designed to decrease the number of experiments as well as the prediction variance. The reliability measure is estimated under right censoring scheme by Maximum likelihood estimator (MLE) assuming that lifetime data have an exponential distribution with parameter, λ, depending on the design and stress variables as well as covariates. In order to find the best factor setting that leads to the most reliable design, response surface methodology is applied to construct the final mathematical program. Finally, a numerical example is analyzed by the proposed approach and sensitivity analyses are performed on variables.