Reliability analysis of multicomponent stress–strength reliability from a bathtub-shaped distribution |
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| Authors: | Liang Wang Ke Wu Yogesh Mani Tripathi Chandrakant Lodhi |
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| Affiliation: | aSchool of Mathematics and Statistics, Xi''an Jiaotong University, Xi''an, People''s Republic of China;bSchool of Mathematics, Yunnan Normal University, Kunming, People''s Republic of China;cDepartment of Mathematics, Indian Institute of Technology Patna, Bihta, India |
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| 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. |
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| Keywords: | Multicomponent stress-strength model bathtub-shaped distribution likelihood estimation pivotal quantity generalized estimation |
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