Nonparametric predictive inference for system reliability using the survival signature

Abstract

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On the structure function and survival signature for system reliability

“…. , l K ), this is also presented by Coolen et al [10]. There may be further ways to learn the survival signature for large systems, for example through simulations, this is an important topic for future research.…”

“…quite straightforward application of Bayesian statistical methods, where F k (t) may be assumed to belong to a parametric family but where also nonparametric approaches are possible, both are illustrated by Aslett et al [2]. Coolen et al [10] illustrate nonparametric predictive inference [3,6] for the system survival function using equation (2), where the ciid assumption is not made and with the generalization to imprecise probabilities [4]. Feng et al [12] illustrate the use of the survival signature combined with known sets of probability distributions for the failure times of the components of different types, so also within theory of imprecise probability [4], and they also discuss computation of importance measures for components in the systems using the survival signature.…”

“…Currently it looks feasible to calculate the survival signature for systems with quite a reasonable number of components, of course it depends on the actual system structure and the number of different component types, but systems with in the order of 100 components should be feasible and we expect that exact calculation methods for larger systems will become available soon. It should be noticed that the survival signature for a system that consists of two subsystems in either series or parallel configuration can be derived from the survival signatures of the subsystems, as shown by Coolen et al [10], using a similar method as presented by Gaofeng et al [13] for Samaniego's signature. Furthermore, the fact that the survival signature Φ(l 1 , .…”

Imprecise system reliability using the survival signature

“…We illustrate this NPI method for system reliability using the survival signature in Example 2 (Coolen, Coolen-Maturi, & Al-nefaiee 2014).…”

“…NPI provides a solution to some explicit goals formulated for objective (Bayesian) inference, which cannot be obtained when using precise probabilities (Coolen 2006), and it never leads to results that are in conflict with inferences based on empirical probabilities. NPI for system survival functions, using the survival signature, was recently presented (Coolen, Coolen-Maturi, & Al-nefaiee 2014) and is briefly summarized here. We now present NPI lower and upper survival functions for the failure time T S of a system consisting of multiple types of components, using the system signature combined with NPI for Bernoulli data (Coolen 1998).…”