Optimum Allocation Rule for Accelerated Degradation Tests With a Class of Exponential-Dispersion Degradation Models

Abstract

Optimum allocation problem in accelerated degradation tests (ADTs) is an important task for reliability analysts. Several researchers have attempted to address this decision problem, but their results have been based only on specific degradation models. Therefore, they lack a unified approach toward general degradation models. This study proposes a class of exponential dispersion (ED) degradation models to overcome this difficulty. Assuming that the underlying degradation path comes from the ED class, we analytically derive the optimum allocation rules (by minimizing the asymptotic variance of the estimated q quantile of product's lifetime) for two-level and three-level ADT allocation problems whether the testing stress levels are prefixed or not. For a three-level allocation problem, we show that all test units should be allocated into two out of three stresses, depending on certain specific conditions. Two examples are used to illustrate the proposed procedure. Furthermore, the penalties of using nonoptimum allocation rules are also addressed. This study demonstrates that a three-level compromise plan with small proportion allocation in the middle stress, in general, is a good strategy for ADT allocation. Supplementary materials for this article are available online.

• Accelerated degradation tests (ADTs)
• Optimum allocation
• V-optimality
• Exponential dispersion model

ACKNOWLEDGMENTS

The authors are grateful to the editor, associate editor, and anonymous referees for many insightful suggestions that significantly improve the quality of this article. The authors thank Prof. Chia-Jung Chang for her useful comments and suggestions. The work was partially supported by the National Science Council (grant no. NSC-102-2118-M-007-001-MY3), MOE 5Y5B project (Contract no. 102N2074E1), and National Center for Theoretical Sciences (NCTS) of Taiwan, Republic of China (ROC).