Nonparametric inference for the stress-strength model under right censoring

Abstract

The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength model is demanding, although lacking. We propose a nonparametric method for the inference of the stress-strength model when the observations are subject to right censoring. The asymptotic properties are also established. The practical utility of the proposed method is assessed through both simulated and real data sets.In the context of reliability, the stress-strength model refers to a component which has a random strength Y and is subject to a random stress X . The component fails if the stress applied to it exceeds the strength, while the component works whenever X Y ∧ .Thus, ( ) P X Y ∧ , denoted by R , could be considered as a measure of component reliability. As another typical application, R could also be used to evaluate the survival strength comparison between two different clinical arms when X and Y are the survival times in each group. See Kotz, Lumelskii, and Pensky [1] for comprehensive introduction.Extensive work has been conducted to assess R when X and Y are independent random variables with identical distribution. Under assumption that X and Y are independently and normally distributed, Church, Harris [2] and Downtown [3] derived the maximum likelihood estimator and the uniformly minimum variance unbiased estimator, respectively. Tong [4] investigated the case in which X and Y are independent exponential random variables. Raqab, Madi, and Kundu [5] further discussed the independent generalized exponential distributions. For the Weibull distribution, see Kundu and Raqab [6] . Constantine and Karson [7] considered the estimation of R when X and Y are independent Gamma random variables. Furthermore, Ali et al [8] considered the estimation of R when X and Y are distributed as two independent four-parameter generalized Gamma random variables. Raqab and Kundu [9] consid-