Modeling of the aging process in stress-strength models

Modeling of the aging process of a component or a system can be performed in various ways. The reliability function is one of the helpful tools commonly used for such modeling. Under specified conditions, the reliability of a component or a system can be defined as the probability that an item will perform satisfactorily, for a given period time. An important method for improving the reliability of a system is to build redundancy into it. A common structure of redundancy is the k-out-of-n system. Both parallel and series systems are special cases of the k-out-of-n system. A series system is equivalent to a 1-out-of-n system while a parallel system is equivalent to an n-out-of-n system.In this thesis, the reliability of parallel, series and k-out-of-n: F systems with exchangeable components in the stress-strength model are considered. It is assumed that a random stress common to all the components in the system level. Applications of obtained results to illustrate the reliability for the system consisting of three components using the multivariate FGM and multivariate Marshall-Olkin distributions are given. Also, examples for the series and parallel systems are presented with some bivariate distributions.