Network Reliability

Chapter 5

Reliability Evaluation using MVI Techniques

Generally, for large and complex systems, reliability evaluation is quite a cumbersome and time-consuming process due to the large number of terms in the resulting reliability expression. Thereafter, the process of assessing numerical value from the obtained expression makes evaluation of accurate value of system reliability a difficult task due to the build-up of round-off error. However, the methods based on sum of disjoint product (SDP) technique have been used to tackle reliability evaluation problems more efficiently and effectively to produce a compact reliability expression. It should further be noted that this disjoint form of expression has a one-to-one mapping with the probability (reliability) expression as well (Aggarwal et al., 1975a), (Aggarwal et al., 1975b). In fact, with the advent of multiple inversions techniques, a new impetus has been given to the techniques of network reliability evaluation using path/cut sets of the network to produce a minimized form of expression. More compact the reliability expression is, more it would help tackle larger and larger system by reducing computational burden, storage requirement and the round off errors.

In this chapter, MVI based approaches KDH88 (Heidtmann, 1989) and CAREL (Soh & Rai, 1991) are presented. Other two approaches (HM–1 and HM–2) (Chaturvedi & MIsra, 2002) to evaluate reliability of large and complex systems by integrating the best features of several efficient ...