On Closure of the IFR Class Under Formation of Coherent Systems

A representation is derived for the failure rate of an arbitrary s-coherent system when the lifetimes of its components are s-independently distributed according to a common absolutely continuous distribution F. The system failure rate is written explicitly as a function of F and its failure rate. The representation is used in several examples, including an example showing that the closure theorem for k-out-of-n systems in i.i.d. IFR components proven by Barlow & Proschan cannot be extended to all s-coherent systems. The class of s-coherent systems for which such closure obtains is characterized.