Review of recent advances in reliability of consecutive <i>k</i>-out-of-<i>n</i> and related systems

Eryılmaz, Serkan

doi:10.1243/1748006xjrr332

“…For systems with only one type of component, the signature has been derived for some specific system structures [26,27,28,36]. Deriving the survival signature for specific system structures in the case of multiple component types is an interesting topic for research.…”

Section: Discussionmentioning

confidence: 99%

“…An attractive feature of describing system structures through signatures is the possibility to compare the reliability of different systems based on stochastic ordering of their signatures, as long as the failure times of all components in these systems are exchangeable [33]. A detailed introduction and overview to system signatures is presented by Samaniego [36], some recent advances are reviewed by Eryilmaz [26].…”

Section: Introductionmentioning

confidence: 99%

Nonparametric predictive inference for system reliability using the survival signature

Coolen

¹

,

Coolen‐Maturi

²

,

Al-Nefaiee

³

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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“…orderings in which the m components can fail must be considered [3,16]. Explicit expressions for the signature of some specific system structures are available [12], but general algorithms to compute signatures have not received much attention in the literature, with the noticeable exception of a logical approach presented by Boland [3] which uses the concept of minimal ordered cut sets, reducing the total number of orderings that need to be counted by grouping together orderings which share the same minimal ordered cut set. However, as any computational method has to deal with the very large number of orderings, it is interesting to consider if one really needs to know the exact signature for a specific inference on the system's reliability.…”

Section: Partially Known Signaturesmentioning

confidence: 99%

“…Subsystem A is the same system, consisting of 7 components (numbered 1-7), as considered in Example 1. Subsystem B consists of 10 components (numbered [8][9][10][11][12][13][14][15][16][17]. While the exact signature for this full system can be obtained by using the given signature for Subsystem A together with repeated use of the algorithm presented by Gaofeng et al [13] for Subsystem B and for the combination of the two subsystems, we assume, in order to illustrate the use of the bounds on signatures presented in this paper, that the signatures of subsystems A and B have only been derived partially, with the bounds and corresponding pessimistic and optimistic signatures as presented in Table 2.…”

Section: Examples Examplementioning

confidence: 99%

Nonparametric predictive inference for system failure time based on bounds for the signature

Al-Nefaiee

¹

,

Coolen

²

2013

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. for the system failure time, given failure times of tested components. However, deriving the system signature is computationally complex. This paper presents how limited information about the signature can be used to derive bounds on such lower and upper survival functions and related inferences. If such bounds are sufficiently decisive they also indicate that more detailed computation of the system signature is not required.

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“…Recent advancements using the concept of system signature are reported in [4]. However the use of the system signature is associated with the assumption that all components in the system are of the same type.…”

Section: Introductionmentioning

confidence: 99%

Imprecise system reliability and component importance based on survival signature

Geng

¹

,

Patelli

²

,

Beer

³

et al. 2016

Reliability Engineering & System Safety

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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 concept of the survival signature has recently attracted increasing attention for performing reliability analysis on systems with multiple types of components.It opens a new pathway for a structured approach with high computational efficiency based on a complete probabilistic description of the system. In practical applications, however, some of the parameters of the system might not be defined completely due to limited data, which implies the need to take imprecisions of component specifications into account. This paper presents a methodology to include explicitly the imprecision, which leads to upper and lower bounds of the survival function of the system. In addition, the approach introduces novel and efficient component importance measures. By implementing relative importance index of each component without or with imprecision, the most critical component in the system can be identified depending on the service time of the system. Simulation method based on survival signature is introduced to deal with imprecision within components, which is precise and efficient. Numerical example is presented to show the applicability of the approach for systems.

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Review of recent advances in reliability of consecutive k-out-of-n and related systems

Cited by 67 publications

References 71 publications

Nonparametric predictive inference for system reliability using the survival signature

Nonparametric predictive inference for system reliability using the survival signature

Nonparametric predictive inference for system failure time based on bounds for the signature

Imprecise system reliability and component importance based on survival signature

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