Boltzmann-like Entropy in Reliability Theory

Rocchi, Paolo

doi:10.3390/e4050142

Cited by 14 publications

(9 citation statements)

References 4 publications

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“…In particular we mean to calculate the effects of repairs and maintenance processes under general assumptions. This work follows two articles previously published on the same vein of research [2,3].…”

Section: Introductionmentioning

confidence: 82%

Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Rocchi¹,

Tsitsiashvili²

2012

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Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal properties of repairable/maintainable systems using the Boltzmann-like entropy. In particular we calculate the reparability function and next discuss the physical meanings of the formal results. Lastly we comment on the broad range of applications and researches which can relate to this study.

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Section: Introductionmentioning

confidence: 82%

Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Rocchi¹,

Tsitsiashvili²

2012

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“…Formally, the generic state Ai (i = 1, 2, … m) is equipped with n sub-states: Ai = (Ai1 AND Ai2 AND … AND Ain), n > 0 (5) We consider that the states of the stochastic system S can be more or less reversible [9], and mean to calculate the reversibility property using the Boltzmann-like entropy Hi where Pi is the probability of Ai:…”

Section: A Lesson From Thermodynamicsmentioning

confidence: 99%

Reshaping the Science of Reliability with the Entropy Function

Rocchi

Capacci

2015

Entropy

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Abstract:The present paper revolves around two argument points. As first, we have observed a certain parallel between the reliability of systems and the progressive disorder of thermodynamical systems; and we import the notion of reversibility/irreversibility into the reliability domain. As second, we note that the reliability theory is a very active area of research which although has not yet become a mature discipline. This is due to the majority of researchers who adopt the inductive logic instead of the deductive logic typical of mature scientific sectors. The deductive approach was inaugurated by Gnedenko in the reliability domain. We mean to continue Gnedenko's work and we use the Boltzmann-like entropy to pursue this objective. This paper condenses the papers published in the past decade which illustrate the calculus of the Boltzmann-like entropy. It is demonstrated how the every result complies with the deductive logic and are consistent with Gnedenko's achievements.

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“…Then, it is possible to use the algorithm determining the path with the least number of edges instead of the algorithm determining the shortest path. 2 To this end, each edge of length kh, k = 1, . .…”

Section: Remarkmentioning

confidence: 99%

“…Under certain constraints on the distribution tail area of the operation time of individual paths, the distribution tail area of the operation time of the entire graph is defined by the slowest failing path. If the times of failure-free operation of the edges have weibullized distributions [1,2], then under some assumptions the asymptotics of the distribution tail area of the time of graph operation is defined by the quickest failing edge of the slowest failing path. Therefore, the asymptotic methods enable substantial simplification of calculations with the use of the logical-and-probabilistic approach to modeling [3,4].…”

Section: Introductionmentioning

confidence: 99%

10.1007/s10513-008-1016-9

2000

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For a network in the form of a connected graph with independent times of failurefree operation of individual edges and singled out initial and terminal vertices, an asymptotic study of the distribution tail area of the time of failure-free network operation was carried out. Formulas expressing this asymptotics in terms of the asymptotics of the distribution of the failure-free operation time of individual edges were obtained. These formulas simplify substantially the calculations and can be used in the studies of the lengths of life cycles of complex systems.

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Boltzmann-like Entropy in Reliability Theory

Abstract: Abstract:We introduce the entropy function in order to study the reliability and repairability of systems. In detail we establish the explicit relationships between reliability and repairability; then we calculate the decay of a system due to its regular running.

Cited by 14 publications

References 4 publications

Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Four Common Properties of Repairable Systems Calculated with the Boltzmann-Like Entropy

Reshaping the Science of Reliability with the Entropy Function

10.1007/s10513-008-1016-9

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