Generalized top and bottom binary n-tuples

Abstract

A complex stochastic Boolean system (CSBS) depends on an arbitrary number n of random Boolean variables. The behavior of a CSBS is determined by the ordering between the occurrence probabilities Pr {u} of the 2 n associated binary strings u ∈ {0, 1} n. In this context, a binary n-tuple is called top (bottom, respectively) if its occurrence probability is always among the 2 n-1largest (smallest, respectively) ones. In this paper we generalize these n-tuples by defining and studying the k-top and k-bottom binary n-tuples, i.e., those whose occurrence probabilities are always among the k largest (smallest, respectively) ones (1 < k < 2 n). These results can be applied to the reliability analysis of many different technical systems, arising from diverse fields of Engineering. © 2008 Civil-Comp Press.