Optimal sample size allocation for multi-level stress testing with Weibull regression under Type-II censoring

Abstract

We discuss the optimal allocation problem in a multi-level stress test with Type-II censoring and Weibull (extreme value) regression model. We derive the maximum-likelihood estimators and their asymptotic variance–covariance matrix through the Fisher information. Four optimality criteria are used to discuss the optimal allocation problem. Optimal allocation of units, both exactly for small sample sizes and asymptotically for large sample sizes, for two- and four-stress-level situations are determined numerically. Conclusions and discussions are provided based on the numerical studies.

Keywords:

• lifetime data
• extreme value distribution
• maximum-likelihood estimators
• Weibull distribution
• survival analysis
• accelerated life testing

Acknowledgements

The authors thank the Editor, Professor Dr O. Bunke, and an anonymous referee for their critical comments and helpful suggestions, which led to a considerable improvement in the contents as well as the presentation of this manuscript. This research is supported by The Research Grants Council of Hong Kong General Research Fund (project number 2150567) and direct grant of Faculty of Science of the CUHK (project number 2060333).