Importance of system components and fault tree events

Barlow, Richard E.; Proschan, Frank

doi:10.1016/0304-4149(75)90013-7

Cited by 282 publications

(162 citation statements)

References 6 publications

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“…Some bounds are obtained in [20], and various computation methods can be found, in another context, in [6] and [25]. From now on we restrict our work in proving some properties for the Ω measure, and in giving an axiomatic characterization of it.…”

Section: Example 22 (Example 11 Revisited)mentioning

confidence: 99%

An axiomatic characterization of the potential decisiveness index

Freixas

Pons

2015

Journal of the Operational Research Society

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Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and let us assume that for achieving this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces in the probability to pass the issue at hand, is a good tool to get the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is showed.

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Section: Example 22 (Example 11 Revisited)mentioning

confidence: 99%

An axiomatic characterization of the potential decisiveness index

Freixas

Pons

2015

Journal of the Operational Research Society

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“…The system availability in stationary state is represented mathematically by the structure function [4,27]:…”

Section: The System Structure Functionmentioning

confidence: 99%

“…where BI i is the i-th system component BI measure (20); q i is probability of the i-th system failure (1) and U is the system's unavailability (4). Dynamic Reliability Indices (DRI).…”

Section: Importance Measuresmentioning

confidence: 99%

“…One of mathematical model is the structure function of a system that is defined by one-to-one mapping of system state and states of the system components. The structure function can be interpreted as Boolean function if the initial system has two possible states as functioning and failure only and the system analysed in the stationary state [4,32]. Therefore mathematical methods of Boolean algebra can be used for the structure function analysis and as result for estimation of system availability.…”

Section: Introductionmentioning

confidence: 99%

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Application of logical differential calculus and binary decision diagramin importance analysis

Zaitseva¹,

Levashenko²,

Kostolny³

2015

EiN

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ApplicAtion of logicAl differentiAl cAlculus And binAry decision diAgrAmin importAnce AnAlysisZAstosowAnie logicZnego rAchunku różnicZkowego orAZ binArnego diAgrAmu decyZyjnego w AnAliZie wAżności ZAitsEvA E, LEvAshEnko v, kostoLny J. Application of logical differential calculus and binary decision diagramin importance analysis. Eksploatacja i niezawodnosc -Maintenance and Reliability 2015; 17 (3): 379-388, http://dx

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“…Barlow and Proschan [1] introduced in 1975 an index which measures an importance degree for each component. This index is defined by the n-tuple I BP whose kth coordinate (k ∈ [n]) is the probability that the failure of component k causes the system to fail; that is,…”

Section: Introductionmentioning

confidence: 99%

Computing system signatures through reliability functions

Marichal

Mathonet

2013

Statistics & Probability Letters

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ABSTRACT. It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen, this index can be computed efficiently by integrating the first derivatives of the reliability function of the system along the main diagonal of the unit hypercube. The Samaniego signature of such a system is another important index that can be computed for instance by Boland's formula, which requires the knowledge of every value of the associated structure function. We show how the signature can be computed more efficiently from the diagonal section of the reliability function via derivatives. We then apply our method to the computation of signatures for systems partitioned into disjoint modules with known signatures.

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Importance of system components and fault tree events

Cited by 282 publications

References 6 publications

An axiomatic characterization of the potential decisiveness index

An axiomatic characterization of the potential decisiveness index

Application of logical differential calculus and binary decision diagramin importance analysis

Computing system signatures through reliability functions

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