Stochastic accelerated degradation model involving multiple accelerating variables by considering measurement error

In accelerated degradation tests, products are usually exposed to several environmental variables or operating conditions. This motivates the need for developing an accelerated degradation model involving multiple accelerating variables. Among the current literature, the conventional accelerated degradation models involving multiple accelerating variables have not considered the measurement error, which inevitably exists in practical degradation datasets. Therefore, a Wiener process-based accelerated degradation model that simultaneously considering multiple accelerating variables and measurement error is proposed. Then approximate closed-form expressions for the failure time distribution (FTD) and its percentiles are derived. The expectation maximization (EM) algorithm is adopted to estimate unknown parameters. Moreover, a multivariate normality testing method is developed to test the fitting goodness of the degradation model. Finally, a comprehensive simulation study and a real application are given to validate the proposed method. The result shows that the proposed model can provide precise estimates even for small sample size of approximately five, and the estimated mean square errors (MSEs) of the mean time to failure (MTTF) and the FTD percentile of the proposed model can be improved by at least 70 % compared with those of the reference methods when the sample size is same.