Estimation of Reliability for a Two Component Survival Stress-Strength Model

The reliability function for a parallel system of two identical components is derived from a stress-strength model, where failure of one component increases the stress on the surviving component of the system. The Maximum Likelihood Estimators of parameters and their asymptotic distribution are obtained. Further the Maximum Likelihood Estimator and Bayes Estimator of reliability function are obtained using the data from a life-testing experiment. Computation of estimators is illustrated through simulation study. 1. Introduction Several authors have considered estimation of system reliability based on stress-strength models. Here are a few references of contributions towards these models. Church and Harris [1] considered estimation of reliability from stress-strength relationship. Downton [2] considered the case of estimation of reliability for a stress-strength model under normal distribution. Wani and Kabe [3] have considered the problem of estimation of system reliability where life time of each component has gamma distribution. Constantine et al. [4] considered estimation of stress-strength relationship under the assumption of stress-strength random variables following gamma distribution with known shape parameters. Bhattacharya and Johnson [5] have considered estimation of reliability in a multicomponent stress-strength model. Kunchur and Munoli [6] have considered estimation of reliability for a multicomponent survival stress-strength model based on exponential distribution. Dan and Krausz [7] have obtained inference for a multistep stress-strength model of parallel system. Kunchur and Munoli [8] have considered estimation of reliability in Freund’s model for a two component system. Hanagal [9] has considered the problem of estimation of system reliability in a two component stress-strength model with cases on distribution of stress as exponential and gamma. Kundu and Gupta [10] have obtained inference of stress-strength relationship for generalized exponential scale family of distribution. Bhattacharya [11] has proposed Bayesian approach to life-testing and reliability estimation. Draper and Guttman [12] have obtained the Bayes estimator of reliability in a multicomponent stress-strength model. In the present study, we are considering a system of two components. The component survives as long as the stress on it is smaller than its strength. The system survives if at least one component functions (parallel system). Here the stress and strength associated with the components of the system are random variables. To carry out the inference, we assume