A mathematical model to evaluate the unavailability of a technical system

Abstract

A new algebraic method is presented for obtaining lower and upper bounds on the unavailability of a technical system depending on n statistically independent random Boolean variables. The efficiency is based on the selection of binary n-tuples (system elementary states) with occurrence probabilities as large as possible. For this purpose: (i) We only select binary n-tuples whose occurrence probabilities are always among the 2 n-1 largest ones, the so-called Top binary n-tuples (which can be characterized by several simple positional criteria). (ii)We provide a simple, recursive formula (tightly related to the famous Pascal's triangle) for rapidly computing the sums of the occurrence probabilities of the binary n-tuples with weight m whose 1s are placed among the k right-most positions (1 ≤ m ≤ k ≤ n).