Analysis of dynamic reliability of the repairable k-out-of-n system under several times random shocks

The model of unit dynamic reliability of the reparable k-out-of-n system is given under several times random shocks with the strength of unit degradation according to the strength-stress theory and the unit failure probability can be observed by using the dynamic reliability. The unit failure number can be obtained under several times random shocks according to the unit failure probability. The conversion probability of the reparable k-out-of-n system is given by its Markov property under several random shocks. The probability density matrix is observed by the conversion probability, and then the dynamic reliability of the reparable k-out-of-n system is obtained by solving the differential equation systems. Finally, it is illustrated that the method is prachcable and convenient. The calculated result conforms to the engineering practice.