Reliability Analysis Of Simply Mixed Repairable System Under Common-Cause Failure

Since in1957the report of Advisory Group on Reliability of Electronic Equipment of The United States Department of Defense, Reliability has been builded up. Now repairable question is important. Because reliability theory’s.requests are strict in mathematical tools, reliability math is the one of reliability theory. Repairable system is the one of reliability theory. By boundary condition whether has integration and initial condition whether is in field of definitions or not repairable system has been divided into. In this paper, Reliability Analysis of Simply Mixed Repairable System which initial is in the field of definitions which boundary condition has not integration condition, under more important Failure (Common-Cause Failure) is researched. By the semi-group theory, integral and differential equation of the system which is described turn to Cauchy’s problem of the space of Banach. Through0is a simple eigenvalue proved by algebraic method and so on, system’s stability is proved. Through discussing the Simply Mixed Repairable System, we can find a distinction between warning function and no warning function. The warming system approximate to a system (no warning function) with mild solution, as hazard rate approaches to infinity. We prove the relative error tends to0with steady-state of warning system and non-warning system by computer. By excessive computation causes and so on, instantaneous availability is preliminarily discussed.