Bivariate degradation modeling and reliability evaluation of accelerometer based on physics- Statistics model and copula function

Abstract

The failure mechanism of modern product has been becoming more complicated. Many highly reliable products usually have complex structure and many functions. They may have two or more performance characteristics. All the performance characteristics can reflect the product's performance degradation over time. What's more, the degradations of performance characteristics may be dependent. Therefore, it is an urgent problem how to describe the multiple performance degradation, establish reliability model of products, and eventually propose a corresponding reliability evaluation method. Bivariate degradation is a special form of multivariate degradation. But it's the most important and fundamental situation. Bivariate degradation analysis is the basis of multiple degradation. To solve this issue, this paper we take a certain type of accelerometer as the research object, selecting two typical performance parameters: scale factor and bias factor and using the accelerated degradation test data for reliability analysis. Here, we build physical statistical models based on physical model and Brownian motion to describe the degradation paths of these two performance characteristics separately. The dependence of the performance characteristics can be described by copula function. After these work, we give out the joint distribution function of the performance characteristics. In order to estimate the product's reliability as accurate as possible, the parameters of the joint distribution function are estimated as a whole. As the model is very complicated and analytically intractable, we use the Bayesian Markov chain Monte Carlo method to simulate the maximum likelihood estimates, which allows the maximum-likelihood estimates of the parameters to be determined in an efficient manner. Finally the reliability function is deduced through the joint distribution of degradations and reliability function of the each performances characteristics. At the end of paper, the effectiveness of the proposed method is verified through accelerometer accelerated stress test.