Comparisons of Coherent Systems' Lifetimes in the Increasing Convex Order

Stochastic orders have been widely used in reliability literature to compare the performances of coherent systems, and various criteria have been provided on this purpose. In particular, sufficient conditions have been found for the lifetime of a system to be stochastically larger than that of another system having the same components with identically distributed lifetimes but a different structure function. Known results of this kind concern some of the most relevant stochastic orders, but in the literature no conditions have been provided for the well-known increasing convex order (icx). Here we describe conditions such that two lifetimes of coherent systems are comparable in this stochastic sense when conditions for other stronger orders do not apply. Illustrative examples are also given.