# Dynamic reliability evaluation for a multi-state component under stress-strength model

Volume 10, Issue 2, pp 377--385
Publication Date: February 20, 2017 Submission Date: November 23, 2016
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### Authors

Sinan Çalık - Department of Statistics, Faculty of Science, Fırat University, 23119 Elazığ, Turkey.

### Abstract

For many technical systems, stress-strength models are of special importance. Stress-strength models can be described as an assessment of the reliability of the component in terms of $X$ and $Y$ random variables where $X$ is the random ”stress” experienced by the component and $Y$ is the random ”strength” of the component available to overcome the stress. The reliability of the component is the probability that component is strong enough to overcome the stress applied on it. Traditionally, both the strength of the component and the applied stress are considered to be both time-independent random variables. But in most of real life systems, the status of a stress and strength random variables clearly change dynamically with time. Also, in many important systems, it is very necessary to estimate the reliability of the component without waiting to observe the component failure. In this paper we study multi-state component where component is subjected to two stresses. In particular, inspired by the idea of Kullback-Leibler divergence, we aim to propose a new method to compute the dynamic reliability of the component under stress-strength model. The advantage of the proposed method is that Kullback-Leibler divergence is equal to zero when the component strength is equal to applied stress. In addition, the formed function can include both stresses when two stresses exist at the same time. Also, the proposed method provides a simple way and good alternative to compute the reliability of the component in case of at least one of the stress or strengths quantities depend on time.

### Keywords

• Kullback-Leibler divergence
• dynamic reliability
• stress-strength model
• multi-state component
• gamma distribution.

•  62N05
•  62F10

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