Review of reliability bounds for consecutive-k-out-of-n systems

Beiu, Valeriu; Dăuş, Leonard

doi:10.1109/nano.2014.6968048

Cited by 10 publications

(7 citation statements)

References 37 publications

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“…(3) Can we find a close approximation to F k (r, n, j) which would be more efficient than computing the number directly? Such approximations are used widely in engineering for F k (2, n, j) [11]. We offer the following conjecture that may be useful in obtaining helpful approximations.…”

Section: Discussionmentioning

confidence: 99%

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Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles

Billings,

Clifton,

Hiller

et al. 2020

Preprint

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Section: Discussionmentioning

confidence: 99%

“…There are many useful and beautiful generalizations of this problem in both reliability theory and graph theory [7,8,9,1,10,11].…”

Section: Introductionmentioning

confidence: 99%

Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles

Billings,

Clifton,

Hiller

et al. 2020

Preprint

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“…In [24], the series and parallel architectures are used to calculate reliability laws and failure rates of different alternatives for multilevel converters. Recent studies on peculiar reliability aspects of k-out-of-n systems are reported in [25]- [26].…”

Section: Extensions To the K-out-of-n Redundant Systemsmentioning

confidence: 99%

Some Basic Properties of the Failure Rate of Redundant Reliability Systems in Industrial Electronics Applications

Chiodo

Lauria

2015

IEEE Trans. Ind. Electron.

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The paper discusses some common reliability architectures, such as "parallel" and "k-out-of-n" systems, adopted to add redundancy in many modern industrial systems, such as parallel-inverter systems. The focus is on some crucial properties of the failure rate of such systems, motivated by the fact that, in applied literature, the system failure rate is often simply evaluated as the reciprocal of the "Mean Time To Failure" of the system. However, this relationship is valid if, and only if, the system has a "series" reliability architecture. This is indeed the only case in which also the system has a constant failure rate, i.e. an Exponential lifetime distribution. Instead, the system failure rate of redundant systems is a function of time, which can never be constant. It is simply shown indeed that the failure rate of a parallel system with constant failure rate components is an increasing, or "first increasing, then decreasing" function of time, eventually reaching the value of the smallest failure rate. These results are extended to "k-out-of-n" reliability systems, and also to more general reliability models with non-constant failure rate, such as the Weibull or the "bathtub" model.

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“…Such bounds have been found which are close approximations to the exact value of R(k, n; q) and which are also much easier to evaluate than the exact value of R(k, n; q). In [DB114], [BD14] and [DB214] the authors compare many such results from the 1980s to the present day.…”

Section: Introductionmentioning

confidence: 99%