CHAPTER 5 - Reliability of k-out-of-n Systems

ABSTRACT This chapter is an exposition of the recent developments in the evaluation of k-out-of-n system reliability. Careful attention is paid to ensure a clarity of presentation and a uniform treatment of the algorithms surveyed and to point out similarities, differences and interrelations among them. Moreover, all the algorithms discussed are analyzed so as to improve them whenever possible and to set measures of comparison among them. The discussion includes formulas for the case of equal-reliability components, several approximate methods as well as conventional and improved techniques based on inclusion-exclusion, disjoint products, pivoting (factoring), and generating functions. Pivoting leads to some recursive relations based on which several recursive algorithms are developed. The most efficient algorithms described are iterative algorithms that are based on generating functions or binary recursion, and that have nice interpretations in terms of very regular signal flow graphs. In the worst case, the temporal and spatial complexities of these algorithms are shown to be quadratic and linear, respectively, in the number of system components. The chapter concludes with a highlight of new trends and developments in the area of k-out-of-n system reliability and closely related areas.

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