The reliability analysis of repairable k-out-of-n systems with component lifetimes and repair time subjected to phase-type distribution

This research investigates a k-out-of-n system in which the lifetime of operational and standby components, the repair time follow continuous phase-type (PH) distribution, instead of exponential distribution or others typical distributions. The proposed paper provides an analytic reliability model that is more suitable to characterize the real situation. The stationary distribution is built by using matrix analytic methods; and several reliability measures of interest are obtained, such as the system stationary availability, system up period, mean time between failures (MTBF) and mean number of failures per unit time (MNF). Finally, a numerical example is presented which implements the applicability and calculability of the model and demonstrate how system reliability measures are influenced by parameter k when n is fixed.