The structure function for system reliability as predictive (imprecise) probability

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractIn system reliability, the structure function models functioning of a system for given states of its components. As such, it is typically a straightforward binary function which plays an essential role in reliability assessment, yet it has received remarkably little attention in its own right. We explore the structure function in more depth, considering in particular whether its generalization as a, possibly imprecise, probability can provide useful further tools for reliability assessment in case of uncertainty. In particular, we consider the structure function as a predictive (imprecise) probability, which enables uncertainty and indeterminacy about the next task the system has to perform to be taken into account. The recently introduced concept of 'survival signature' provides a useful summary of the structure function to simplify reliability assessment for systems with many components of multiple types. We also consider how the (imprecise) probabilistic structure function can be linked to the survival signature. We briefly discuss some related research topics towards implementation for large practical systems and networks, and we outline further possible generalizations.

Simulation methods for system reliability using the survival signature

“…In order to verify the correctness of Algorithm 3 which is based on survival signature, the results have been compared with the solution of simulation method based on the structural function. The minimum path sets of the Bridge system shown in Figure 2 are [1,2,3], [1,2,5,6], [1,3,4,5] and [1,4,6]. N = 5000 samples have been used to estimate the reliability of the system and the results shown in Figures 8 and 10 are in perfect agreement with the results obtained using Algorithm 3.…”

“…it might be composed by an additional component of type 1 or two components of type 2 connected in parallel. However, the system can still be described using the survival signature although a↵ected by imprecision [6]. This has the advantages of more realistic reflections of uncertainty on system functioning and the proposed imprecision, only one Monte Carlo simulation would have been required to analyse the system with imprecision in the survival signature.…”

“…In order to overcome the limitations of the system signature, Coolen and Coolen-Maturi [5,6] presented the survival signature, which has the same merits as the system signature for systems consisting of a single type of components, but it is also an e↵ective tool for analysing complex systems consisting of multiple component types. Therefore, the survival signature is a useful tool for reliability quantification for complex systems and networks because it only needs to be calculated once providing a massive reduction of the computational cost required by the analysis.…”

On the structure function and survival signature for system reliability

“…System functioning can have many meanings here: for example it may mean that the car will satisfactorily enable us to travel to our destination today, or function without problems the next week, or any other criterion. Recently, we considered such scenarios and proposed to focus explicitly on a next task, also enabled by the use of a probabilistic structure function [9]. This also makes it possible to consider vaguely specified or unknown tasks, in particular through the further generalisation of the structure function as an imprecise probability [4].…”

“…The derivation of the survival function may become harder (e.g. the fast approach using binary decision diagrams [15] depends on the binary nature of the structure function), but the main equation (1) remains the same if the structure function is a probability, and even the generalization of the survival signature corresponding to the use of imprecise probabilistic 8 structure functions is quite straightforward [9].…”