Strategic allocation of test units in an accelerated degradation test plan

Abstract

Degradation is often defined in terms of the change of a key performance characteristic over time. When the degradation is slow, accelerated degradation tests (ADTs) that apply harsh test conditions are often used to obtain reliability information in a timely manner. It is common to see that the initial performance of the test units varies and it is strongly correlated with the degradation rate. Motivated by a real application in the semiconductor sensor industry, this study advocates an allocation strategy in ADT planning by capitalizing on the correlation information. In the proposed strategy, the initial degradation levels of the test units are measured and the measurements are ranked. The ranking information is used to allocate the test units to different factor levels of the accelerating variable. More specifically, we may prefer to allocate units with lower degradation rates to a higher factor level in order to hasten the degradation process. The allocation strategy is first demonstrated using a cumulative-exposure degradation model. Likelihood inference for the model is developed. The optimum test plan is obtained by minimizing the large sample variance of a lifetime quantile at nominal use conditions. Various compromise plans are discussed. A comparison of the results with those from traditional ADTs with random allocation reveals the value of the proposed allocation rule. To demonstrate the broad applicability, we further apply the allocation strategy to two more degradation models which are variants of the cumulative-exposure model.

Keywords:

• compromise test plan
• general path model
• large sample approximate variance
• order statistics
• random initial degradation
• reliability

About the authors

Dr. Ye is Assistant Professor in Department of Industrial Systems Engineering & Management, National University of Singapore. His email address is: [email protected]

Dr. Hu is Associate Professor in Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His email address is: [email protected]

Dr. Yu is Professor in Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His email address is: [email protected]

Acknowledgments

We are grateful to the Editor and two referees for their insightful comments that have led to a substantial improvement on an earlier version of the paper.

Additional information

Funding

Dr. Ye was partially supported by the Natural Science Foundation of Jiangsu Province (BK20180232). Dr. Hu and Dr. Yu were partly supported by the National Key R&D Programs of the Ministry of Science and Technology of China (2018YFB0704304), the National Center for Mathematics and Interdisciplinary Sciences (CAS), and the Key Laboratory of Systems and Control (CAS).