Bivariate Degradation Reliability Modeling And Experimental Design Approaches Under Accelerating Stress Scenarios

Reliability modeling based on performance degradation, which is an important technique to tackle lifetime prediction for products characterized as small sample, highly reliable and long life, becomes a new research field of reliability theory. With the development of science and technology, the failure mechanism of products becomes more and more complicated. Many highly reliable products have more than one performance characteristics and all of them degrade with time. However, these degradation processes are not independent, so it is exigent and difficult to describe the multivariate degradation information, to build reliability model based on performance degradation, and to propose relevant lifetime prediction and design approach of degradation test for highly reliable products. Bivariate degradation is a special case of multivariate degradation, but it is the most essential and important case. Therefore, this thesis focuses on the highly reliable products with two correlative performance characteristics and investigates the degradation modeling, reliability estimation and optimal design for degradation test under accelerating stress scenarios. The proposed models and approaches will be used to tackle the problems in engineering practice. The main achievements are as follows.(1) Bivariate degradation modeling approaches based on Wiener processes under constant-stress accelerating scenarios are discussed. For the products with two relevant performance characteristics, we use Wiener processes and Copulas to describe the degradation failure processes and their correlativity, respectively. The bivariate degradation models based on Wiener processes under normal operating stress and constant-stress accelerating scenarios and the corresponding parameters estimation methods are presented. After that, we make use of these models and methods to deal with the rubidium consumption and light attenuation modeling of rubidium discharge lamp and estimate their reliability.(2) Bivariate degradation modeling approaches based on Gamma processes under constant-stress accelerating scenarios are presented. The degradation failure processes of many highly reliable products with two relevant performance characteristics are strictly monotone, that is, the degradation increments are non-negative, and the degradation processes strictly increase. We take advantage of Gamma processes to meet this case. The bivariate degradation models based on Gamma processes under normal operating stress and constant-stress accelerating scenarios are presented. And the bivariate Birnbaum-Saunders distribution and its marginal distributions are used to denote the reliability model of the products. The proposed models and methods are validated through the fatigue cracks development of the alloy products.(3) Bivariate degradation modeling approaches under step-stress accelerating scenarios are investigated. For a newly developed or very expensive product where only a few test units are available, we should consider obtaining their performance degradation information by step-stress accelerated degradation test. Hence, we present the bivariate degradation modeling method based on Wiener and Gamma processes under step-stress accelerating scenarios and provide an effective route for step-stress accelerated degradation test data. Furthermore, we discuss the effects of acceleration model misspecification on the precision of the MTTF prediction in step-stress accelerated degradation test for single performance characteristic, which lays a foundation for multivariate case.(4) Optimal design approaches for the bivariate degradation test under accelerating stress scenarios are proposed. For the highly reliable products with two relevant performance characteristics, we investigate the optimal design approaches for the bivariate degradation test and corresponding algorithms for solving the models under constant-stress and step-stress accelerating scenarios. We also analyze the effects on test plans of the changes of model parameters and stress levels and analyze the effects on model parameters estimation of changes of test plans in detail. The proposed methods provide a solution for optimal design of the bivariate degradation test under accelerating stress scenarios.