The concept of the signature of a coherent system is useful to study the stochastic and aging properties of the system. Let $X_{1:n},X_{2:n},\ldots,X_{n:n}$ denote the ordered lifetimes of the components of a coherent system consisting of $n$ i.i.d components. If $T$ denotes the lifetime of the system, then the signature vector of the system is defined to be a probability vector ${\bf s}=(s_{1},s_{2},\ldots,s_{n})$ such that $s_{i}=P(T=X_{i:n})$, $i=1,2,\ldots,n$. Here we consider a coherent system with signature of the form ${\bf s}=(s_{1},s_{2},\ldots s_{i},0\ldots,0)$, where $s_{k}>0$, $k=1,2,\ldots,i$. Under the condition that the system is working at time $t$, we propose a time dependent measure to calculate the probability of residual life of live components of the system, i.e., $X_{k:n}$, $k=i+1,\ldots,n$. Several stochastic and aging properties of the proposed measure are explored.