Advanced Data Analysis and Test Planning for Highly Reliable Products

Abstract

Accelerated life testing (ALT) has been widely used in collecting failure time data of highly reliable products. Most parametric ALT models assume that the ALT data follows a specific probability distribution. However, the assumed distribution may not be adequate in describing the underlying failure time distribution. In this dissertation, a more generic method based on a phase-type distribution is presented to model ALT data. To estimate the parameters of such Erlang Coxian-based ALT models, both a mathematical programming approach and a maximum likelihood method are developed. To the best of our knowledge, this dissertation demonstrates, for the first time, the potential of using PH distributions for ALT data analysis. To shorten the test time of ALT, degradation tests have been studied as a useful alternative. Among many degradation tests, destructive degradation tests (DDT) have attracted much attention in reliability engineering. Moreover, some materials/products start degrading only after a random degradation initiation time that is often not even observable. In this dissertation, two-stage delayed-degradation models are developed to evaluate the reliability of a product with random initiation time. For homogeneous and heterogeneous populations, fixed-effects and random-effects Gamma processes are considered, respectively. An expectation-maximization algorithm and a bootstrap method are developed to facilitate the maximum likelihood estimation of model parameters and to construct the confidence intervals of the interested reliability index, respectively. With an Accelerated DDT model, an optimal test plan is presented to improve the statistical efficiency. In designing the ADDT experiment, decision variables related to the experiment must be determined under the constraints on limited resources, such as the number of test units and the total testing time. In this dissertation, the number of test units and stress level are pre-determined in planning an ADDT experiment. The goal is to improve the statistical efficiency by selecting appropriately allocate the test units to different stress levels to minimize the asymptotic variance of the estimator of the p-quantile of failure time. In particular, considering the random degradation initiation time, a three-level constant-stress destructive degradation test is studied. A mathematical programming problem is formulated to minimize the asymptotic variance of reliability estimate.