Reliability Analysis Of A Two Components Repairable System With Priority

The thesis is devoted to study the stabilization of a repairable systemthat consists of two dissimilar components with component1has priority inuse and repair by semigroup theory and Laplace transform method.Firstly, suppose that the life of each component satisfies the exponentiallydistribution and the repair time of the component satisfies a general distribu-tion, the component1has priority in use and repair, and the elapse repairedtime on component2will be valid if the repair be ceased. Based on this, amathematical model is built via the diferential and partial diferential equa-tions by the supplement variable technique. Then by the spectral analysis,some basic results such as the existence and uniqueness of the solution, thenon-negative steady state solution and the exponential stability of the systemare derived. Especially, the rapidity of convergence of the dynamic solution tothe steady state is be estimated under certain condition which has not beenobtained in other papers. By contrasted with the system the elapse repairedtime on component2be invalid if the repair be ceased and must be started re-pairing from the very beginning, some results show the diference between thetwo systems. Moreover, based on the stability result, an optimization problemabout the normal availability of the system will be discussed.Secondly, for the repairable system, the cost will be high after a certaintime repair, and some system should be guaranteed a certain availability atall cost. Thus, the replace policy will be employed. Then a new model will bebuilt for the repairable system considered in the former section, by semigrouptheory, the well-possedness, asymptotic stability and the exponential stabilityof the system are also derived. Diferent from the system without replacepolicy, the spectrum is only composed of point spectrum. Furthermore, basedon the stability result, we will study the evolution of steady state availabilitywith the development of the replace time. Thirdly, most repairable systems are deteriorating because of the agingefect and accumulative wear or the degeneration of repair technology. Con-sequently, a deteriorating model is taken into account. To speak specifically,suppose the component1cannot be repaired “as good as new” after failures,and component2is still“as good as new” after failures for convenience, accord-ing to the repair times of component1, the deteriorating model is set up. ByLaplace transform method, some important indices of the system reliabilityin accordance with the fact are derived, such as the system availability, theprobability of the repairman working and the rate of occurrence of failures.