Reliability comparison of systems of different orders using pseudo-signatures

Abstract

Comparison among a number of systems of same or different orders is a very common issue to the reliability practitioners. Various methods and criteria for the said purpose are available in the literature, but are not applicable to all system designs. The signature of a system with independent and identically distributed component lifetimes has been found to be very useful in the study and comparison of engineered systems.  But the signatures and tail probability vectors have been used for comparing the systems of same order. The method fails if the systems are of different orders. This paper discusses an approach to comparing the systems of different orders by introducing a new distribution-free measure. Even if the component reliabilities are not known or the reliability function is difficult to evaluate, this method shows a way to compare the reliabilities of the systems in order to select the best one for which reliability is maximum.