Comparison among several commonly used sampling methods for a degradation test

摘要

Degradation testing is an effective tool for evaluating the reliability of highly reliable products. There have been many data collection methods proposed in the literature. Some of these assumed that only degradation values are recorded, and some assumed failure times to be available. However, most research has been devoted to proposing parameter estimates or to designing degradation tests for a specific sampling method. The differences between these commonly used methods have rarely been investigated. The lack of comparisons between different sampling methods has made it difficult to select an appropriate means by which to collect data. In addition, it remains unclear whether obtaining extra information (eg, exact failure times) is useful for making statistical inferences. In this paper, we assume that the degradation path of a product follows a Wiener degradation process, and we summarize several data collection methods. Maximum likelihood estimates for parameters and their variance-covariance matrices are derived for each type of data. Several commonly used optimization criteria for designing a degradation test are used to compare estimation efficiency. Sufficient conditions under which one method could be better than the others are proposed. Upper bounds of estimation efficiency are also investigated. Our results provide useful guidelines by which to choose a sampling method, as well as its design variables, to obtain efficient estimation. A simulated example based on real light-emitting diodes data is studied to verify our theoretical results under a moderate sample size scenario.