Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, for r-out-of-n systems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.
"Stochastic comparisons of residual lifetimes and inactivity times of coherent systems." J. Appl. Probab. 50 (3) 848 - 860, September 2013. https://doi.org/10.1239/jap/1378401240