Simulation methods for system reliability using the survival signature

Abstract

Recently, the survival signature has been presented as a summary of the structure function which is su cient for computation of common reliability metrics and has the crucial advantage that it can be applied to systems with components whose failure times are not exchangeable. The survival signature provides a huge reduction in required information, e.g. for its storage, compared to the full structure function, its implementation to larger systems is still di cult in a purely analytical manner and simulations may be required to derive the reliability metrics of interest. Hence, the main question addressed in this paper is whether or not the survival signature provides su cient information for e cient simulation to derive the system's failure time distribution. We answer this question in the a rmative by presenting two algorithms for survival signature-based simulation. In addition, we present a third simulation algorithm that can be used in case of repairable components. It turns out that these algorithms are very e cient, beyond the initial advantage of requiring only the survival signature to be available, instead of the full structure function.

System reliability and component importance when components can be swapped upon failure

“…It may be of interest to investigate whether or not this change can also be reflected by a distortion of the component reliabilities, which may provide a further tool for comparison of different systems and different swapping routines. It has been shown that very efficient simulation methods can be based on the survival signature; the same simulation method can perhaps also be used to only learn about difference in reliability for two swapping regimes. In ongoing research, the authors are including cost considerations for enabling or actually executing swaps and costs corresponding to system down time to decide on optimal swapping regimes.…”

“…The survival signature is closely linked to Samaniego's system signature for systems with a single type of components, and it is particularly useful for larger systems with only a few different types of components. Recently, the survival signature has attracted considerable interest from researchers in reliability, who have considered both mathematical properties and aspects of application, including statistical inference, comparison of different systems, and fast simulation methods . In this paper, we will consider scenarios where some components of the same type can be swapped and we use the survival signature to derive the corresponding system reliability.…”

Mean residual life of coherent systems consisting of multiple types of dependent components

“…Reed (2017) proposed an efficient algorithm to compute survival signature of a system. Patelli, Feng, Coolen, and Coolen-Maturi (2017) presented a simulation method for system reliability using the survival signature.…”

On the structure function and survival signature for system reliability

“…To get further insight into the system survival function for complex systems, when analytical derivations are not feasible anymore, the ability to perform simulations efficiently is crucial. Patelli et al [14] show that the survival function is sufficient for such simulations, where different algorithms can be used depending on whether one aims explicitly at simulating system failure times or at learning the system survival function. In particular for the latter scenario the survival signature allows extremely efficient simulation.…”