Exploiting symmetry in the reliability analysis of coherent systems

Abstract

In practice, components in a complex system are not structurally identical. However, we may often find some components that have similar structure positions, and hence one should make use of this piece of information in studying reliability problems. For example, in practical reliability engineering, components are usually in series with each other. There is no need to calculate the structural importance for all these components because all components that are in series with each other will have the same structural importance. In this article we will introduce a definition of symmetry and present a study of this concept for system reliability analysis. It will be shown that the idea, although very simple, can be used to simplify reliability computation, and it can also be used to obtain bounds on system reliability. In Section 2, a general definition of symmetric components is given and some characterizations are indicated. In Section 3, we first develop lower and upper bounds on system reliability and then proceed to give some properties concerning component importance measures that can be of practical importance when deciding which component to improve in such a system. In Section 4, some theoretical results on structural properties of systems having symmetric components are summarized. In particular, we show that the symmetry property is preserved by the dual transformation of the structure function. Throughout the article we assume that the basic components in a system are independent. Our notations and terminologies will follow those given by Barlow and Proschan [I]. The systems considered in this article are assumed to be coherent unless otherwise stated.