Inference for the common mean of several Birnbaum–Saunders populations

ABSTRACT

The Birnbaum–Saunders distribution is a widely used distribution in reliability applications to model failure times. For several samples from possible different Birnbaum–Saunders distributions, if their means can be considered as the same, it is of importance to make inference for the common mean. This paper presents procedures for interval estimation and hypothesis testing for the common mean of several Birnbaum–Saunders populations. The proposed approaches are hybrids between the generalized inference method and the large sample theory. Some simulation results are conducted to present the performance of the proposed approaches. The simulation results indicate that our proposed approaches perform well. Finally, the proposed approaches are applied to analyze a real example on the fatigue life of 6061-T6 aluminum coupons for illustration.

KEYWORDS:

• Coverage probability
• generalized inference
• hypothesis test
• interval estimation
• reliability

Acknowledgments

The authors are grateful to the editor, the associate editor and two anonymous referees for constructive comments and suggestions that led significant improvement of an early manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Xu Guo's research was supported by the Fundamental Research Funds for the Central Universities [grant no. NR2015001] and the Natural Science Foundation of Jiangsu Province, China [grant no. BK20150732]. Gaorong Li's research was supported by the National Natural Science Foundation of China [grant no. 11471029], the Beijing Natural Science Foundation [grant no. 1142002] and the Science and Technology Project of Beijing Municipal Education Commission [grant no. KM201410005010].