Reliability analysis of multicomponent stress–strength reliability from a bathtub-shaped distribution

Abstract

In this paper, inference for a multicomponent stress–strength model is studied. When latent strength and stress random variables follow a bathtub-shaped distribution and the failure times are Type-II censored, the maximum likelihood estimate of the multicomponent stress–strength reliability (MSR) is established when there are common strength and stress parameters. Approximate confidence interval is also constructed by using the asymptotic distribution theory and delta method. Furthermore, another alternative generalized point and confidence interval estimators for the MSR are constructed based on pivotal quantities. Moreover, the likelihood and the pivotal quantities-based estimates for the MSR are also provided under unequal strength and stress parameter case. To compare the equivalence of the stress and strength parameters, the likelihood ratio test for hypothesis of interest is also provided. Finally, simulation studies and a real data example are given for illustration.

Keywords:

• Multicomponent stress-strength model
• bathtub-shaped distribution
• likelihood estimation
• pivotal quantity
• generalized estimation

Acknowledgments

The authors would like to thank the editor and two referees for their insightful comments that have led to a substantial improvement to an earlier version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was of Liang Wang is supported by the China Postdoctoral Science Foundation[grant number 2019M650260], the National Natural Science Foundation of China [grant number 11501433] and Ministry of Education of Humanities and Social Science project [grant number 18YJC910009]. The work of Yogesh Mani Tripathi is partially supported by Science and Engineering Research Board, India [grant number EMR/2016/001401].