# A Copula Based Stress-Strength Reliability Estimation with Lindley Marginals

### Abstract

The stress-strength model is a basic tool used in evaluating the reliability (R). It shows that a component or system with stress (Y) and strength (X) will fail if the stress exceeds the strength, and its counterpart allows it to function. Usually, the statistical independence between X and Y are assumed and reliability models are extensively developed in the literature. However, in real life, there are many situations in which the dependence stress-strength is taken into account. So it is important to consider and model the association between them. In this paper, we estimated R when the stress and strength parameters are linked by a Fralie-Gumble-Morgenstern copula with Lindley marginals. The estimates of reliability and dependence parameter are obtained by using maximum likelihood estimation (MLE), inference function margins (IFM), and semi parametric (SP) methods. In addition, the length of the asymptotic confidence interval and the coverage probability of the dependence parameter are also computed. A simulation study is performed to evaluate the effectiveness of the various estimates, and a real data set is also used for illustrative purposes.

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