Reliability Analysis with Ill-Known Probabilities and Dependencies

Abstract

In this work, we are interested in estimating the uncertainty that a system will work, given the probabilities that its components will be either failing or working. Usually, this estimation is done by propagating the component uncertainties through a structure function. This problem is well-studied when component probabilities are known and when the component are assumed to be independent. In this paper, we first recall some results obtained when considering that probabilities are unknown and when one either assume component independence or no knowledge about the components dependence. We also explore some structures not studied up to now, such as consecutive k-out-of-n structures.

State distribution and reliability of some multistate systems with complex configurations

“…Belaloui and Ksir (2007) established a non recursive formula for computing the exact reliability of multi-state consecutive k-outof-n : G systems without constraints on M or on k j for all j (1 ≤ j ≤ M ). Usually most of the studies assume independence among components, because computation of reliability characteristics of a system that consists of dependent components is difficult especially when a specific type of dependence is not known Destercke et al (2014), Eryilmaz (2009. In the present work, since each one of the both (consecutive k n -out-of-m n : G series and consecutive k n -out-of-m n : G parallel) systems is compound of blocks, and in order to reach the previous declared goal, we proceed as follows: we evaluate the reliability of each block which has the multi-state consecutive k n -out-of-m n : G configuration (n = 1, 2, ..., N ), then we extend the method to get the reliability of the global system.…”