Computing system signatures through reliability functions

Marichal, Jean-Luc; Mathonet, Pierre

doi:10.1016/j.spl.2012.11.018

“…This study can be regarded as the continuation of Marichal and Mathonet [8], where (22) and (23), Algorithm 5, and Proposition 5 were already presented and established. component lifetimes, and we have extended theses formulae to the general dependent case.…”

Section: Discussionmentioning

confidence: 97%

Algorithms and Formulae for Conversion Between System Signatures and Reliability Functions

Marichal

2015

J. Appl. Probab.

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The concept of a signature is a useful tool in the analysis of semicoherent systems with continuous, and independent and identically distributed component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For such systems, we provide conversion formulae between the signature and the reliability function through the corresponding vector of dominations and we derive efficient algorithms for the computation of any of these concepts from any other. We also show how the signature can be easily computed from the reliability function via basic manipulations such as differentiation, coefficient extraction, and integration.

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“…component lifetimes and we have extended theses formulas to the general dependent case. This study can be regarded as the continuation of paper [8], where Eqs. (22)-(23), Algorithm 5, and Proposition 5 were already presented and established.…”

Section: Discussionmentioning

confidence: 98%

“…(21) gives the polynomial h(x) in terms of vector S. The following proposition yields simple expressions of h(x) and h ′ (x) in terms of vector s. This result was already presented in [6,Sect. 4] and [8,Rem. 2] in alternative forms.…”

Section: Proposition 5 ([8]) Let (C ϕ) Be An N-component Semicoherementioning

confidence: 99%

Algorithms and Formulae for Conversion Between System Signatures and Reliability Functions

Marichal

2015

Journal of Applied Probability

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The concept of a signature is a useful tool in the analysis of semicoherent systems with continuous, and independent and identically distributed component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For such systems, we provide conversion formulae between the signature and the reliability function through the corresponding vector of dominations and we derive efficient algorithms for the computation of any of these concepts from any other. We also show how the signature can be easily computed from the reliability function via basic manipulations such as differentiation, coefficient extraction, and integration.

show abstract

“…Proof of Proposition 5. On the one hand, setting k = 1 in (10) and (11) shows that d 1 = α 1 and d D 1 = β 1 . On the other hand, setting k = 2 in (10), we obtain Proof of Proposition 6.…”

Section: − J∈[r]mentioning

confidence: 99%