Reliability Analysis Of Repairable Multi-state Degraded Systems

Repairable multi-state degraded system is an important system in reliability theory,which is widely used in production systems, power systems and so on. Because ofpractical demand, maintenance policy is one of the essential parts in a repairablemulti-state degraded system, while maintenance policy can have an important influence onthe system reliability indices and the economic benefit of the system. Therefore,multi-state degraded system with different maintenance policy has theoretical significanceand application value.In this paper, we consider the repairable multi-state degraded system model. Themain contents are as follows:Firstly, reliability analysis of the repairable multi-state degraded system model withminimal repairs and the replacement policy is presented. The model is the expansion ofthe repairable multi-state degraded system which has been studied in reference. Throughutilizing Markov process theory and Laplace transform method, we derive the Laplacetransformation of the instantaneous availability and the failure frequency, and expressionsof the reliability, the mean time to first failure, the steady-state availability and thesteady-state failure frequency. In addition, we also discuss several performance indicesand reliability problems under the condition that the replacement function is distributedgenerally.Secondly, reliability analysis of the repairable multi-state degraded system modelwith minimal repairs and the imperfect preventive maintenance is studied. The model isthe improvement of the repairable multi-state degraded system model with minimalrepairs and the imperfect preventive maintenance which has been studied in reference. Byutilizing Markov process theory and Laplace transform method, we derive the Laplacetransformation of the reliability, the mean time to first failure, the instantaneousavailability and the failure frequency, and the expressions of the steady-state availabilityand the steady-state failure frequency.Lastly, we develop the repairable multi-state degraded system model with minimal repairs, the imperfect preventive maintenance, and replacement policy. The model is theexpansion of the repairable multi-state degraded system which has been studied inreference. By utilizing broad Markov process theory and Laplace transform method, wederive the differential equations, by which the reliability indices such as the reliability aregained. And then according to a specific model, we derive the Laplace transform of theinstantaneous availability and the failure frequency, and the expressions of the steady-stateavailability and the steady-state failure frequency.