Characterizations of the Relative Behavior of Two Systems via Properties of Their Signature Vectors

Block, Henry W.; Dugas, Michael R.; Samaniego, Francisco J.

doi:10.1007/0-8176-4487-3_18

Cited by 7 publications

(10 citation statements)

References 4 publications

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“…The proof is obtained by applying Theorem 18.3.1 in Block et al [3] to the representation in (2.6). Similar signaturebased characterizations may be obtained for the hazard rate and likelihood ratio orders.…”

Section: Dynamic Signatures For a Working System With K Failed Componmentioning

confidence: 98%

“…Using results from Block et al [3], it is possible to obtain conditions on dynamic signatures that fully characterize these relations. The following result, for example, provides necessary and sufficient conditions for the stochastic ordering of residual lifetimes in part (a) of the preceding theorem to hold.…”

Section: Dynamic Signatures For a Working System With K Failed Componmentioning

confidence: 98%

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Dynamic signatures and their use in comparing the reliability of new and used systems

Samaniego

Balakrishnan

Navarro

2009

Naval Research Logistics

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Abstract:The signature of a system with independent and identically distributed (i.i.d.) component lifetimes is a vector whose ith element is the probability that the ith component failure is fatal to the system. System signatures have been found to be quite useful tools in the study and comparison of engineered systems. In this article, the theory of system signatures is extended to versions of signatures applicable in dynamic reliability settings. It is shown that, when a working used system is inspected at time t and it is noted that precisely k failures have occurred, the vector s ∈ [0, 1] n−k whose j th element is the probability that the (k + j)th component failure is fatal to the system, for j = 1, 2, . . . , n − k, is a distribution-free measure of the design of the residual system. Next, known representation and preservation theorems for system signatures are generalized to dynamic versions. Two additional applications of dynamic signatures are studied in detail. The well-known "new better than used" (NBU) property of aging systems is extended to a uniform (UNBU) version, which compares systems when new and when used, conditional on the known number of failures. Sufficient conditions are given for a system to have the UNBU property. The application of dynamic signatures to the engineering practice of "burn-in" is also treated. Specifically, we consider the comparison of new systems with working used systems burned-in to a given ordered component failure time. In a reliability economics framework, we illustrate how one might compare a new system to one successfully burned-in to the kth component failure, and we identify circumstances in which burn-in is inferior (or is superior) to the fielding of a new system.

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Section: Dynamic Signatures For a Working System With K Failed Componmentioning

confidence: 98%

Section: Dynamic Signatures For a Working System With K Failed Componmentioning

confidence: 98%

Dynamic signatures and their use in comparing the reliability of new and used systems

Samaniego

Balakrishnan

Navarro

2009

Naval Research Logistics

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“…These results are the subject of the present section. The results below are based on arguments found in Block, Dugas and Samaniego [10]. We first consider an NASC for the stochastic ordering of system lifetimes.…”

Section: Signature-based Characterizations Of Relative System Performmentioning

confidence: 99%

System Signatures and their Applications in Engineering Reliability

Samaniego

2007

International Series in Operations Research &Amp; Management Science

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398

359

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“…[3], [4], [5], [6], [15], and [19,Chapters 4,5]) and in the analysis of network reliability (see, e.g. [8] and [10]).…”

Section: Notation Definitions and Basic Factsmentioning

confidence: 99%

“…lifetimes of the N different modules; thus, by applying to each module (3) and (4) with F (t) replaced by G(t), we can writē…”

Section: Signatures Of Recurrent Systemsmentioning

confidence: 99%

Signatures of Coherent Systems Built with Separate Modules

2011

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The signature is an important structural characteristic of a coherent system. Its computation, however, is often rather involved and complex. We analyze several cases where this complexity can be considerably reduced. These are the cases when a 'large' coherent system is obtained as a series, parallel, or recurrent structure built from 'small' modules with known signature. Corresponding formulae can be obtained in terms of cumulative notions of signatures. An algebraic closure property of families of homogeneous polynomials plays a substantial role in our derivations.

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Characterizations of the Relative Behavior of Two Systems via Properties of Their Signature Vectors

Cited by 7 publications

References 4 publications

Dynamic signatures and their use in comparing the reliability of new and used systems

Dynamic signatures and their use in comparing the reliability of new and used systems

System Signatures and their Applications in Engineering Reliability

Signatures of Coherent Systems Built with Separate Modules

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