Planning Repeated Degradation Testing for Products With Three-Source Variability

Repeated degradation testing data have been widely used to assess lifetime of highly-reliable products or components with scarce failures. In this paper, we consider the problem of planning repeated degradation testing for products exhibiting three-source variability in their degradation characteristics, including the temporal variability, unit-to-unit variability, and measurement variability. The primary objective of this paper is centered on deciding the amount of units and the measurement schedule to achieve required estimation precision for some important statistics of interest. In such a planning process, the testing budget is limited and used as a constraint of an optimization model. To do so, a kind of Wiener degradation process, which has a random drift coefficient and a constant volatility coefficient, is used to model the repeated degradation testing data, where the measurement errors are considered and described as additive zero-mean random variables. Under the presented modeling framework, the lifetime distribution is formulated under the concept of the first passage time of the stochastic degradation process. Then, the large-sample approximate standard errors of the maximum likelihood estimations for the mean failure time and the quantile of the degradation distribution are derived, respectively. Furthermore, the constrained optimization model, which incorporates the cost of each degradation measurement, is proposed to plan the degradation testing by minimizing the testing cost under the condition of a maximum acceptable approximate standard error. Finally, an example is provided to illustrate the procedure and advantages of the presented method.