The Research Of Repairable System With Repairing Is Not As Good As New

Repairable system is one of the most important systems discussed in the reliability theory. In the study of traditional repairable system, we always discuss the reliability and stability of the system under ideal condition, that is the system can be repaired as good as new. But in actually, many units can’t be repaired in a few time, and also can’t be repaired as good as new.Based on the above reason, we established human error modeling of two identical units parallel repairable system with repairing is not as good as new by using supplementary variable method. Firstly, the proof of existence and uniqueness of nonnegative solution of the system is given, by converting model equations into Volterra equation in Banach space. Secondly, we transfer model equations into a abstract Cauchy problem by choosing state space and defining operator of system, proved the operator of the system generates a positive contraction Co-semigroup in Banach space. Moreover, we obtained0is simple eigenvalue with nonnegative eigenvector by discussing the distribution of spectral of the system operator and it’s dual operator, and proved the asymptotic stability of the system. Thirdly, we discussed the reliability indicators of the system by the reliability theory and obtained the availability of the system reduce as the repair cycle of system increases. Finally, we searched the steady-solution and solid reliability of the system which can be repaired as good as new, by using the supplementary remaining time variable technique and the method of Laplace-transform.