COMPARISONS OF PARALLEL SYSTEMS ACCORDING TO THE CONVEX TRANSFORM ORDER.

A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics from heterogeneous and homogeneous exponential samples in the sense of the dispersive order and the right- spread order are established. A sufficient condition is also given for the proportional hazard rate model. [ABSTRACT FROM AUTHOR]