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 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 The Joint Signature of Coherent Systems with Shared Components

2010 ◽  
Vol 47 (1) ◽  
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 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 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.

Algorithms and Formulae for Conversion Between System Signatures and Reliability Functions

2015 ◽  
Vol 52 (02) ◽  
pp. 490-507
Author(s):  
Jean-Luc Marichal
Keyword(s):  
System Reliability ◽  
Reliability Function ◽  
Efficient Algorithms ◽  
System Designs ◽  
Independent And Identically Distributed

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.

On the equivalence of systems of different sizes, with applications to system comparisons

2016 ◽  
Vol 48 (2) ◽  
pp. 332-348 ◽  
Author(s):  
Bo H. Lindqvist ◽  
Francisco J. Samaniego ◽  
Arne B. Huseby
Keyword(s):  
Optimization Problem ◽  
Coherent System ◽  
Sufficient Condition ◽  
Equivalent System ◽  
Coherent Systems ◽  
Two Systems ◽  
Equivalent Systems ◽  
Engineered Systems ◽  
Signature Vector ◽  
Mixed Systems

Abstract The signature of a coherent system is a useful tool in the study and comparison of lifetimes of engineered systems. In order to compare two systems of different sizes with respect to their signatures, the smaller system needs to be represented by an equivalent system of the same size as the larger system. In the paper we show how to construct equivalent systems by adding irrelevant components to the smaller system. This leads to simpler proofs of some current key results, and throws new light on the interpretation of mixed systems. We also present a sufficient condition for equivalence of systems of different sizes when restricting to coherent systems. In cases where for a given system there is no equivalent system of smaller size, we characterize the class of lower-sized systems with a signature vector which stochastically dominates the signature of the larger system. This setup is applied to an optimization problem in reliability economics.

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