Conditionalk-out-of-nsystems with a cold standby component

In this article, we consider a k-out-of-n system with a cold standby component under the general condition that lth (0 < l ⩽ n − k + 1) component is working at time t. The survival function and mean residual life function of such system are derived. Some stochastic monotonic properties of the system lifetimes are presented as well. Numeric results are provided to illustrate the results. The main results obtained in this article complement and generalize related ones in Eryilmaz (2012 Eryilmaz, S. (2012). On the mean residual life of a k-out-of-n: G system with a single cold standby component. Eur. J. Oper. Res. 222:273–277.[Crossref], [Web of Science ®] , [Google Scholar]).