The reliability analysis of multi-state cold standby system based on phase-type distribution

The multi-state cold standby system with two identical units has a single repair facility that provides two kinds of service: preventive maintenance and corrective maintenance according to the state of units, and the corrective maintenance has a higher priority. The continuous Phase-type distribution, instead of exponential distribution or other typical distributions, are used to described the residence time in the different performance of the operational unit, the preventive maintenance time and the corrective maintenance time. The proposed analytic model is more suitable to characterize the real situation. The stationary distribution is built by using matrix analytic methods; and several performance measures of interest, such as the system stationary availability, operational time, mean time between failures (MTBF), failure arrival rate of repair facility and system failure rate, are obtained. Finally, the validity and applicability of the model are implemented by numerical applications.