Description
Appearing on the scene in the late 1940s and early 1950s, reliability was first defined and applied to communication and transportation, and it has become a major part of performance measure for military systems. Much of the early work was confined to reliability analysis, and many of the early theories were developed hypothetically without considering the real problems encountered.
Along with reliability design, the concept of importance measures of components in a coherent system was proposed in the 1960s (Birnbaum 1969). At that moment, the system of interest was confined to a binary system of two states, functioning or failed. Strictly, the early version of the importance measures was sensitivity analysis of a probabilistic system. Given the increasing trend of using complex and complicated systems, other types of importance measures have also been investigated, one of which is the Fussell–Vesely importance (Fussell 1975; Vesely 1970), which was used in the design for reliability and safety in nuclear power plants. The precise relationships among various importance measures and their applications in the areas of reliability, risk, mathematical programming, and even broader categories have not yet been investigated thoroughly. This book will be the first to meet the need of addressing these unresolved issues.
In the 1980s, consecutive-k-out-of-n (Con/k/n) systems were proposed as a type of complex systems (Chiang and Niu 1981). It was quickly studied that optimal design for such systems is nearly impossible without further investigating other types of importance measures. Similarly, applications such as design for reliable software systems were needed, and with the aid of importance measures, one is able to improve software reliability with limited resources (Fiondella and Gokhale 2008). Still, optimal design has been only remotely possible. In the 1990s, as with other optimization design tools, heuristics were proposed along with importance measures to facilitate optimal reliability design (Kuo and Prasad 2000; Kuo and Wan 2007).