Journal of Systems Science and Complexity

, Volume 28, Issue 5, pp 1015–1032

# Reliability analysis of a cold standby repairable system with repairman extra work

• Xin Zhang
Article

## Abstract

This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The authors are devoted to studying the unique existence and exponential stability of the system solution. C 0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

## Keywords

C0-semigroup exponential stability repairable system resolvent positive operator

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