Reliability Analysis Of Irreparable As Good As New Multi-state Series System

Reliability theory is a comprehensive discipline which treat characteristics of the productlife as the main research object, and reliability mathematics is one of the most important basictheory of reliability theory. In recent years, having been widely used in various fields of military,economy and so on,the reliability of research is of great importance.The two components series connection repairable system is one of the basic modes in thetheory of reliability. On the base of the existing research harvest, this paper has studied thereliability analysis of two systems as follows: The two components series connection repairablesystem with inspection cycle. It is assumed that each component of the system has normal,abnormal and failure three modes(the normal mode and abnormal mode both are operativemode),and none component of the system can attain the failure mode without passing throughthe abnormal mode, and the system is checked to make sure the components are in normal modeor abnormal mode if it is operating, and the component life, its repair time both have exponentialdistribution,and it can not be repaired as good as new. By using total probability decomposition,the supplement variable method, Lapalce transform and Lapalce-stietjes transform, a series ofimportant reliability characteristics are obtained, such as the system’s instantaneous availability,steady-state availability, the abnormal frequency, and the failure frequency, and the method ofcalculating the optimal inspection cycle is obtained.