Abstract:

This paper presents several useful mixture representations for the reliability function of the residual live of a coherent system with independent but non-identically distributed components. These presentations are based on order statistics, signatures and mean reliability functions. We then discuss some stochastic comparisons of residual lives between two systems based on the stochastic ordering of coefficient vectors (or components) of the two systems. These results form nice extensions of some known results for the case of independent and identically distributed components.