Mean residual life function of a coherent system with known number of failed components

This article considers the mean residual life (MRL) function of a coherent system when the number of failed components of the system is known. We assume that the lifetimes of the system components are independent and identically distributed (iid) random variables and show that when the components of the system have increasing (decreasing) failure rate, that is IFR (DFR), the MRL function of the system is decreasing (increasing) in time. Same property for k-out-of-n systems with independent but not identical (inid) components is also shown when the failed components of the system are known, extending some results in literatures.