The usage of mixture distribution models in system reliability analysis

Estimating the reliability of a system and its components is one of the majorproblems in statistical reliability analysis. In reliability analysis, the shape of life distributions of systems can vary considerably, for example, sometimes failure rate can occur for more than one reason. And there exists statistical dependence between components in many real multicomponent systems. So, it?s desirable to use a flexible lifetime distribution and a mixture distribution is nice tool for modelling such situation. Finite mixtures of distributions have provided a mathematical-based approach to the statistical modeling of a wide variety of random phenomena. Because of their usefulness as an extremely flexible method of modeling, finite mixture models have continued to receive increasing attention over the years, from both a practical and theoretical point of view.The structure of a multi-component system is indicated by a reliability block diagram. In this study, mixture reliability functions, mixture probability density functions and mixture hazard functions were established for reliability block diagrams of series, parallel and complex systems in the absence of dependency between components. By the mixture distribution model approximation to system reliability: function representations were simplified, function calculations were decreased and information extracted from the system and its components were increased for reliability block diagrams of series, paralel and complex systems.This study also includes a mixture model in the event of statistical dependence of components in a two-component system.