Reliability Analysis Of Repairable System With Phase Type Life Or Phase Type Repairs

Reliability analysis has aroused a huge amount of attention in the society, whilenowadays the repairable system has become the focus, which has various strategies, suchas work strategies, repair strategies, vacation strategies and so on. In much of referencedocuments, the life distribution or repair time is assumed to be exponential distributions.Based on the references, the paper has submitted the PH distributions into the repairablemodel, and we obtain the reliability indices of these systems.Firstly, the concept of PH distribution is introduced and one unit repairable system isstudied. The life distribution is assumed to be PH distributions, and the repair time isassumed to be exponential distributions. By using the supplementary variable and thegeneralized Markov progress, we get some important reliability indexes, for example thesystem reliability, system availability and system mean failure time.Secondly, a cold standby system which the repair time of the component is PHdistributions is studied. The system has two-different component. One is a workcomponent, and another is a cold standby component. The life distribution is exponentialdistributions, and the component is assumed that it is “as good as new”. Under theseassumptions, by using the supplementary variable and the generalized Markov progress,some reliability indexes of the system, such as the instantaneous probability distribution,the instantaneous availability, the smooth probability distribution and the steadyavailability are obtained.Thirdly, a collateral system with repairman vacation is studied, which the repair time ofthe component is PH distributions. The system has two-different component. The lifedistribution and vacation time are assumed to be exponential distributions, and the repairtime of the component is assumed to be PH distributions. The component is assumed thatit is “as good as new” after repair. By using the supplementary variable and thegeneralized Markov progress, some reliability indexes of the system, such as theinstantaneous probability distribution, system’s first failure the average time and the steadyavailability are obtained.Finally, a cold standby system which the life distribution is PH distributions is studied. Thesystem has two-different component. The repair time of the component is exponentialdistributions, and the component is assumed that it is “as good as new”. By using the supplementary variable and the generalized Markov progress, some reliability indexes ofthe system are obtained, such as the steady availability and so on.