scholarly journals Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

2011 ◽  
Vol 48 (03) ◽  
pp. 856-867 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Coherent Systems ◽  
Representation Theorems ◽  
Performance Of Systems ◽  
Independent And Identically Distributed

Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

scholarly journals Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

2011 ◽  
Vol 48 (3) ◽  
pp. 856-867 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Coherent Systems ◽  
Representation Theorems ◽  
Performance Of Systems ◽  
Independent And Identically Distributed

Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

scholarly journals The number of failed components in a coherent working system when the lifetimes are discretely distributed

Metrika ◽  
2021 ◽  
Author(s):  
Krzysztof Jasiński
Keyword(s):  
Random Variables ◽  
Continuous Case ◽  
Coherent System ◽  
Coherent Systems ◽  
Discrete Random Variables ◽  
Independent And Identically Distributed

AbstractIn this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

scholarly journals Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

2010 ◽  
Vol 47 (03) ◽  
pp. 876-885 ◽  
Author(s):  
Zhengcheng Zhang
Keyword(s):  
Order Statistics ◽  
Reliability Function ◽  
Coherent System ◽  
Coherent Systems ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

scholarly journals On the Conditional Residual Life and Inactivity Time of Coherent Systems

2014 ◽  
Vol 51 (4) ◽  
pp. 990-998 ◽  
Author(s):  
A. Parvardeh ◽  
N. Balakrishnan
Keyword(s):  
Residual Life ◽  
Coherent System ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we derive mixture representations for the reliability functions of the conditional residual life and inactivity time of a coherent system with n independent and identically distributed components. Based on these mixture representations we carry out stochastic comparisons on the conditional residual life, and the inactivity time of two coherent systems with independent and identical components.

scholarly journals ON THE COMPARISON OF PERFORMANCE-PER-COST FOR COHERENT AND MIXED SYSTEMS

2020 ◽  
pp. 1-18
Author(s):  
Bo H. Lindqvist ◽  
Francisco J. Samaniego ◽  
Nana Wang
Keyword(s):  
Optimal System ◽  
Naval Research ◽  
Coherent Systems ◽  
Comparison Result ◽  
Stochastic Orderings ◽  
Cost Criterion ◽  
Naval Research Logistics ◽  
System Designs ◽  
Mixed Systems ◽  
Independent And Identically Distributed

The present paper is concerned with reliability economics, considering a certain performance-per-cost criterion for coherent and mixed systems, as introduced in [Dugas, M.R. & Samaniego, F.J. (2007). On optimal system designs in reliability-economics frameworks. Naval Research Logistics 54, 568–582]. We first present a new comparison result for performance-per-cost of systems with independent and identically distributed component lifetimes under certain stochastic orderings. We then consider optimization of the performance-per-cost criterion, first reconsidering and refining results from the above cited paper, and then considering mixtures of given subsets of coherent systems.

scholarly journals Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

2010 ◽  
Vol 47 (3) ◽  
pp. 876-885 ◽  
Author(s):  
Zhengcheng Zhang
Keyword(s):  
Order Statistics ◽  
Reliability Function ◽  
Coherent System ◽  
Coherent Systems ◽  
Distributed Components ◽  
Inactivity Time ◽  
Independent And Identically Distributed

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

scholarly journals The Joint Signature of Coherent Systems with Shared Components

2010 ◽  
Vol 47 (01) ◽  
pp. 235-253 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Joint Distribution ◽  
Sufficient Conditions ◽  
Coherent Systems ◽  
Stochastic Orderings ◽  
Similar Concept ◽  
Independent And Identically Distributed

System signatures are useful tools in the study and comparison of coherent systems. In this paper, we define and study a similar concept, called the joint signature, for two coherent systems which share some components. Under an independent and identically distributed assumption on component lifetimes, a pseudo-mixture representation based on this joint signature is obtained for the joint distribution of the lifetimes of both systems. Sufficient conditions are given based on the respective joint signatures of two pairs of systems, each with shared components, to ensure various forms of bivariate stochastic orderings between the joint lifetimes of the two pairs of systems.

scholarly journals On the Residual and Inactivity Times of the Components of Used Coherent Systems

2012 ◽  
Vol 49 (2) ◽  
pp. 385-404 ◽  
Author(s):  
S. Goliforushani ◽  
M. Asadi ◽  
N. Balakrishnan
Keyword(s):  
Dependent Measure ◽  
Time Dependent ◽  
Residual Lifetime ◽  
Coherent System ◽  
Reliability Engineering ◽  
Coherent Systems ◽  
Distributed Components ◽  
Technical Systems ◽  
Stochastic Properties ◽  
Independent And Identically Distributed

In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.

scholarly journals On the Residual and Inactivity Times of the Components of Used Coherent Systems

2012 ◽  
Vol 49 (02) ◽  
pp. 385-404 ◽  
Author(s):  
S. Goliforushani ◽  
M. Asadi ◽  
N. Balakrishnan
Keyword(s):  
Dependent Measure ◽  
Time Dependent ◽  
Residual Lifetime ◽  
Coherent System ◽  
Reliability Engineering ◽  
Coherent Systems ◽  
Distributed Components ◽  
Technical Systems ◽  
Stochastic Properties ◽  
Independent And Identically Distributed

In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.

On the Closure of Aging Classes Under the Formation of Coherent Structures

2021 ◽  
pp. 2140002
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Failure Rate ◽  
Coherent Structures ◽  
Sufficient Conditions ◽  
Failure Criteria ◽  
Closure Property ◽  
Coherent Systems ◽  
Increasing Failure Rate ◽  
Independent And Identically Distributed

In this paper, we study the closure property of the Increasing Failure Rate (IFR) class under the formation of coherent systems. Sufficient conditions for the nonpreservation of the IFR attribute for reliability structures consisting of [Formula: see text] independent and identically distributed ([Formula: see text] components are provided. More precisely, we deal with the IFR preservation (or nonpreservation) under the formation of structures with two common failure criteria by the aid of their signature vectors.

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