Optimum degradation test plan under model mis-specification for Wiener and gamma processes

Abstract

Degradation tests have been used for the purpose of assessing reliability information. In this paper, we consider a degradation test design problem under a statistical model mis-specification scenario. The Wiener and gamma processes are considered in this research. A gamma process is suitable for describing degradation paths that exhibit monotone behavior. However, if one fits a Wiener process model to the data, the resulting statistical inferences may be affected. Tsai, Tseng, and Balakrishnan studied the effect on the estimated mean time to failure. However, the experimental design problem was not discussed. A lack of the explicit functional form of the estimation variances makes it difficult to find degradation plans that can improve test efficiency. In this paper, functional forms of optimal degradation test plans are proposed under model mis-specification. Furthermore, a weighted ratio objective function considering the prior probability of the true model is used to find robust test plans for practical use. The results from a numerical example show that, by using an appropriate degradation test plan, the estimation variance can be reduced, and the test efficiency can be improved. A simulation study is conducted to investigate the performance of the parameter estimates when the sample size is small.

Keywords:

• Degradation test
• Gamma process
• Inverse Gaussian distribution
• Model mis-specification
• Wiener process

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62N05
• 90B25

Acknowledgments

The author would like to thank the Editor and two reviewers for their valuable comments and suggestions that have resulted in a significantly improved paper.

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan (Contract No: MOST 108-2221-E-006-060).