Comparing Birnbaum Importance Measure of System Components

Abstract

This article provides us with some simple criteria to compare Birnbaum reliability importance measure of components in a general binary coherent system. Such criteria are particularly useful in the absence of information concerning component reliabilities. We also find several simple (necessary and sufficient) conditions concerning system structure, under which such comparison is possible. Examples are given to illustrate our results.

Analysis for joint importance of components in a coherent system

“…Importance measures can also be estimated by Monte Carlo simulation [12,13]. The discussion of importance is still a hot topic in reliability field recently, see for example, Levitin [14] and Meng [15]. These importance definitions have been well defined and widely used in reliability engineering practice.…”

On the Formalization of Importance Measures Using HOL Theorem Proving

“…However, this approach requires high computations to obtain the criticality value for all system components and then perform the successive analysis, which may not be possible for large and complex systems. An alternate approach is to verify a relative measure relationship for any pair of components and obtain the necessary conditions, as described by Meng [7].…”

“…For instance, Boland et al [6] developed a relationship stating that the component i is structurally more critical than the component j if its structure function is larger when i is down and j is up as compared to the opposite case. This work is further extended by Meng [7] to obtain the necessary conditions, based on Birnbaum and Fussell-Vesely importance measures, that are essential for proving the analytical relationships describing the relative importance of any pair of system components. These analytical relationships can be extremely helpful in practical scenarios since calculating the exact values of a component importance measures can be tedious for large and complex systems.…”

Birnbaum Reliability Importance for (n,f,k) and ⟨n,k,f⟩ System

“…Kamalja (2012) studied B-importance of consecutive-k-out-of-n:F , m-consecutive-k-out-of-n:F , and r-withinconsecutive-k-out-of-n:F system. A study related to reliability importance of popular systems and various generalizations of B-importance has been reported in Meng (2002, 2009), Hong et al (2002, Fan (2004), Gao et al (2007), Rani et al (2011), etc. Downloaded by [The University Of Melbourne Libraries] at 08:02 10 October 2014…”