Generalizing the Signature to Systems with Multiple Types of Components

Coolen, Frank P. A.; Coolen‐Maturi, Tahani

doi:10.1007/978-3-642-30662-4_8

Cited by 105 publications

(187 citation statements)

References 6 publications

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“…Coolen and Coolen-Maturi [16] introduced the survival signature for such a system, denoted by Φ(l 1 , l 2 , . .…”

Section: The Survival Signaturementioning

confidence: 99%

“…For the special case of a system consisting of only a single type of components, so with all m components exchangeable and K = 1 in the notation above, the survival signature is linked to the signature through the following equality [16] …”

Section: The Survival Signaturementioning

confidence: 99%

“…This equality implies that, for this rather restrictive situation, the survival signature and the signature are effectively the same with just the order of summation in Equation (2) together with Equation (3) exchanged. This implies that all attractive properties of the signature also hold for the method using the survival signature [16], yet the survival signature is also easy to apply for systems with multiple types of components, and one could argue that it is easier to interpret than the signature. The survival signature Φ(l 1 , .…”

Section: The Survival Signaturementioning

confidence: 99%

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Nonparametric predictive inference for system reliability using the survival signature

Coolen

Coolen‐Maturi

Al-Nefaiee

2014

Proceedings of the Institution of Mechanical Engineers, Part O:

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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. AbstractThe survival signature has recently been presented as an attractive concept to aid quantification of system reliability. It has similar characteristics as the system signature, which is well established, but contrary to the latter it is easily applicable to systems with multiple types of components. We present an introductory overview of the survival signature together with new results to aid computation. We develop nonparametric predictive inference for system reliability using the survival signature. The focus is on the failure time of a system, given failure times of tested components of the same types as used in the system.

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“…Coolen and Coolen-Maturi [16] introduced the survival signature for such a system, denoted by Φ(l 1 , l 2 , . .…”

Section: The Survival Signaturementioning

confidence: 99%

Section: The Survival Signaturementioning

confidence: 99%

Section: The Survival Signaturementioning

confidence: 99%

See 1 more Smart Citation

Nonparametric predictive inference for system reliability using the survival signature

Coolen

Coolen‐Maturi

Al-Nefaiee

2014

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…We use the term 'exchangeable components' to indicate that the failure times of the components in the system are exchangeable (De Finetti 1974). Recently, we introduced such a summary, called the survival signature, to facilitate reliability analyses for systems with multiple types of components (Coolen & Coolen-Maturi 2012). In case of just a single type of components, the survival signature is closely related to the system signature (Samaniego 2007), which is well-established and the topic of many research papers during the last decade.…”

Section: Introductionmentioning

confidence: 99%

“…, l K ). Due to the exchangeability assumption for the failure times of the m k components of type k, all the state vectors x k ∈ S k l k are equally likely to occur, hence (Coolen & Coolen-Maturi 2012)…”

Section: Introductionmentioning

confidence: 99%

Imprecise system reliability using the survival signature

Coolen

Coolen‐Maturi

Aslett

et al. 2016

Applied Mathematics in Engineering and Reliability

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The survival signature has been introduced to simplify quantification of reliability of systems which consist of components of different types, with multiple components of at least one of these types. The survival signature generalizes the system signature, which has attracted much interest in the theoretical reliability literature but has limited practical value as it can only be used for systems with a single type of components. The key property for uncertainty quantification of the survival signature, in line with the signature, is full separation of aspects of the system structure and failure times of the system components. This is particularly useful for statistical inference on the system reliability based on component failure times. This paper provides a brief overview of the survival signature and its use for statistical inference for system reliability. We show the application of generalized Bayesian methods and nonparametric predictive inference, both these inference methods use imprecise probabilities to quantify uncertainty, where imprecision reflects the amount of information available. The paper ends with a discussion of related research challenges.

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Signatures of Repairable Systems

Suárez‐Llorens

2019

Wiley StatsRef: Statistics Reference Online

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The literature related to system signatures is briefly discussed. In short, computing a “signature” is associated with the fact of capturing the essence of a coherent system to simplify the quantification of its reliability. In this context, a representation of the reliability function of a repairable coherent system of components is addressed. It is assumed that each component can individually fail and be minimally repaired up to a fixed number of times. Failures occur at any component according to a nonhomogeneous Poisson process with a common intensity function. First, it is shown that the reliability function of a series system can be written in terms of the intensity function and a distribution‐free measure based on the probabilities of the number of repairs until system failure. Secondly, the utility of this result in the comparative study of system performance is illustrated through a “preservation” theorem. Finally, the results for series systems lead to an explicit expression for computing the reliability function of any repairable coherent system that depends on a distribution‐free measure of the system's design.

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Generalizing the Signature to Systems with Multiple Types of Components

Cited by 105 publications

References 6 publications

Nonparametric predictive inference for system reliability using the survival signature

Nonparametric predictive inference for system reliability using the survival signature

Imprecise system reliability using the survival signature

Signatures of Repairable Systems

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