Inferences on the reliability in balanced and unbalanced one-way random models

Abstract

In this article, the hypothesis testing and interval estimation for the reliability parameter are considered in balanced and unbalanced one-way random models. The tests and confidence intervals for the reliability parameter are developed using the concepts of generalized p-value and generalized confidence interval. Furthermore, some simulation results are presented to compare the performances between the proposed approach and the existing approach. For balanced models, the simulation results indicate that the proposed approach can provide satisfactory coverage probabilities and performs better than the existing approaches across the wide array of scenarios, especially for small sample sizes. For unbalanced models, the simulation results show that the two proposed approaches perform more satisfactorily than the existing approach in most cases. Finally, the proposed approaches are illustrated using two real examples.

Keywords:

• reliability parameter
• generalized p-value
• generalized confidence interval
• coverage probability

AMS Subject Classification:

• Primary 62F03
• Secondary 62N05

Acknowledgements

We gratefully acknowledge the editor and referees for their valuable comments and suggestions which greatly improve this paper. This material is based upon work funded by National Natural Science Foundation of China, Tian Yuan Special Foundation (Grant No. 10926059), National Social Science Foundation of China (Grant No. 12CJY012), Zhejiang Provincial Natural Science Foundation of China (Grant Nos. Y6100053, Y6110017), Zhejiang Provincial New Century 151 Talents Project of China (Grant No. ZX120201316006), and Ministry of Education of China, Humanities and Social Science Projects (Grant No. 10YJC790184).