Wang Liang, Wu Ke, Tripathi Yogesh Mani, Lodhi Chandrakant
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, People's Republic of China.
School of Mathematics, Yunnan Normal University, Kunming, People's Republic of China.
J Appl Stat. 2020 Aug 8;49(1):122-142. doi: 10.1080/02664763.2020.1803808. eCollection 2022.
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.
本文研究了多组件应力-强度模型的推断问题。当潜在强度和应力随机变量服从浴盆形分布且失效时间为II型删失时，在存在共同强度和应力参数的情况下，建立了多组件应力-强度可靠性（MSR）的最大似然估计。还利用渐近分布理论和德尔塔方法构建了近似置信区间。此外，基于枢轴量构建了MSR的另一种广义点估计和置信区间估计。此外，在强度和应力参数不相等的情况下，还给出了MSR的似然估计和基于枢轴量的估计。为了比较应力和强度参数的等价性，还给出了感兴趣假设的似然比检验。最后，通过模拟研究和一个实际数据例子进行说明。
