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.

scholarly journals On relative ageing of coherent systems with dependent identically distributed components

2020 ◽  
Vol 52 (1) ◽  
pp. 348-376
Author(s):  
Nil Kamal Hazra ◽  
Neeraj Misra
Keyword(s):  
Sufficient Conditions ◽  
System Level ◽  
Hazard Rates ◽  
Coherent System ◽  
Coherent Systems ◽  
Component Level ◽  
Distributed Components ◽  
Two Systems

AbstractRelative ageing describes how one system ages with respect to another. The ageing faster orders are used to compare the relative ageing of two systems. Here, we study ageing faster orders in the hazard and reversed hazard rates. We provide some sufficient conditions for one coherent system to dominate another with respect to ageing faster orders. Further, we investigate whether the active redundancy at the component level is more effective than that at the system level with respect to ageing faster orders, for a coherent system. Furthermore, a used coherent system and a coherent system made out of used components are compared with respect to ageing faster orders.

On component failure in coherent systems with applications to maintenance strategies

2020 ◽  
Vol 52 (4) ◽  
pp. 1197-1223
Author(s):  
M. Hashemi ◽  
M. Asadi
Keyword(s):  
Partial Information ◽  
Optimal Strategies ◽  
Coherent System ◽  
Coherent Systems ◽  
Component Failure ◽  
Distributed Components ◽  
The Status ◽  
Optimal Maintenance ◽  
Maintenance Policies ◽  
Signature Vector

AbstractProviding optimal strategies for maintaining technical systems in good working condition is an important goal in reliability engineering. The main aim of this paper is to propose some optimal maintenance policies for coherent systems based on some partial information about the status of components in the system. For this purpose, in the first part of the paper, we propose two criteria under which we compute the probability of the number of failed components in a coherent system with independent and identically distributed components. The first proposed criterion utilizes partial information about the status of the components with a single inspection of the system, and the second one uses partial information about the status of component failure under double monitoring of the system. In the computation of both criteria, we use the notion of the signature vector associated with the system. Some stochastic comparisons between two coherent systems have been made based on the proposed concepts. Then, by imposing some cost functions, we introduce new approaches to the optimal corrective and preventive maintenance of coherent systems. To illustrate the results, some examples are examined numerically and graphically.

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 for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components

2013 ◽  
Vol 45 (4) ◽  
pp. 1011-1027 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Representation Theorem ◽  
Joint Distribution ◽  
Survival Function ◽  
Coherent Systems ◽  
Comparative Performance ◽  
Component Failure ◽  
Distribution Free ◽  
Joint Survival Function ◽  
Signature Vector ◽  
New Distribution

The signature of a system is defined as the vector whose ith element is the probability that the system fails concurrently with the ith component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared components. Here, a new distribution-free measure, the ‘joint bivariate signature’, of a pair of systems with shared components is defined, and a new representation theorem for the joint survival function of the system lifetimes is established. The theorem is shown to facilitate the study of the dependence between systems and the comparative performance of two pairs of such systems.

scholarly journals Component importance in coherent systems with exchangeable components

2015 ◽  
Vol 52 (3) ◽  
pp. 851-863 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Importance Measure ◽  
Coherent System ◽  
Coherent Systems ◽  
System A ◽  
Component Importance

This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results.

ON RELATIVE AGING COMPARISONS OF COHERENT SYSTEMS WITH IDENTICALLY DISTRIBUTED COMPONENTS

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Nil Kamal Hazra ◽  
Neeraj Misra
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
Stochastic Orders ◽  
Coherent System ◽  
Coherent Systems ◽  
Cumulative Hazard ◽  
Numerical Examples ◽  
Distributed Components ◽  
Rate Functions ◽  
Important Notion

The relative aging is an important notion which is useful to measure how a system ages relative to another one. Among the existing stochastic orders, there are two important orders describing the relative aging of two systems, namely, aging faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for k-out-of-n systems. Moreover, some numerical examples are given to illustrate the applications of proposed results.

Dynamic balancing of the cleaning unit used in agricultural thresher using a non-dominated sorting Jaya algorithm

2020 ◽  
Vol 37 (5) ◽  
pp. 1849-1864
Author(s):  
Prem Singh ◽  
Himanshu Chaudhary
Keyword(s):  
Optimization Problem ◽  
Dynamic Performance ◽  
A Priori ◽  
Center Of Mass ◽  
Equivalent System ◽  
Jaya Algorithm ◽  
Content Type ◽  
Optimum Parameters ◽  
Design Variables ◽  
Adams Software

Purpose This paper aims to propose a dynamically balanced mechanism for cleaning unit used in agricultural thresher machine using a dynamically equivalent system of point masses. Design/methodology/approach The cleaning unit works on crank-rocker Grashof mechanism. This mechanism can be balanced by optimizing the inertial properties of each link. These properties are defined by the dynamic equivalent system of point masses. Parameters of these point masses define the shaking forces and moments. Hence, the multi-objective optimization problem with minimization of shaking forces and shaking moments is formulated by considering the point mass parameters as the design variables. The formulated optimization problem is solved using a posteriori approach-based algorithm i.e. the non-dominated sorting Jaya algorithm (NSJAYA) and a priori approach-based algorithms i.e. Jaya algorithm and genetic algorithm (GA) under suitable design constraints. Findings The mass, center of mass and inertias of each link are calculated using optimum design variables. These optimum parameters improve the dynamic performance of the cleaning unit. The optimal Pareto set for the balancing problem is measured and outlined in this paper. The designer can choose any solution from the set and balance any real planar mechanism. Originality/value The efficiency of the proposed approach is tested through the existing cleaning mechanism of the thresher machine. It is found that the NSJAYA is computationally more efficient than the GA and Jaya algorithm. ADAMS software is used for the simulation of the mechanism.

Pseudo-modular decompositions and ‘refined bounds’ for the interval reliability and the availability for binary coherent systems

1989 ◽  
Vol 21 (01) ◽  
pp. 91-122
Author(s):  
N. Mazars
Keyword(s):  
Traditional Approach ◽  
Applied Mathematics ◽  
Divide And Conquer ◽  
Second Step ◽  
Coherent System ◽  
Coherent Systems ◽  
Complete Extension ◽  
Interval Reliability

‘Divide and conquer’ is a traditional approach in various fields of applied mathematics. In reliability, only modules have been proposed to decompose complex coherent systems. However, a system may include no modules, except ‘trivial’ ones. This paper is the second step of a study concerned with module generalizations : in the first step, pseudo-modules have been retained as the most general coherent subsystems which can yield a complete extension of the fundamental results concerning modules; in addition, it has been proved that they concern any binary coherent system; in this paper, it is shown that pseudo-modular decompositions are the most general coherent decompositions which can yield a complete extension of all the ‘refined bounds’ for the interval reliability and the availability currently proposed in terms of modular decompositions. This study also yields some fundamental results to extend all the ‘refined bounds’ currently proposed for multistate coherent systems, using an easier approach.

scholarly journals NON-EMPTINESS OF MODULI SPACES OF COHERENT SYSTEMS

2008 ◽  
Vol 19 (07) ◽  
pp. 777-799 ◽  
Author(s):  
L. BRAMBILA-PAZ
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Algebraic Curve ◽  
Coherent System ◽  
Coherent Systems ◽  
Generic Element

Let X be a general smooth projective algebraic curve of genus g ≥ 2 over ℂ. We prove that the moduli space G(α:n,d,k) of α-stable coherent systems of type (n,d,k) over X is empty if k > n and the Brill–Noether number β := β(n,d,n + 1) = β(1,d,n + 1) = g - (n + 1)(n - d + g) < 0. Moreover, if 0 ≤ β < g or β = g, n ∤g and for some α > 0, G(α : n,d,k) ≠ ∅ then G(α : n,d,k) ≠ ∅ for all α > 0 and G(α : n,d,k) = G(α′ : n,d,k) for all α,α′ > 0 and the generic element is generated. In particular, G(α : n,d,n + 1) ≠ ∅ if 0 ≤ β ≤ g and α > 0. Moreover, if β > 0 G(α : n,d,n + 1) is smooth and irreducible of dimension β(1,d,n + 1). We define a dual span of a generically generated coherent system. We assume d < g + n1≤ g + n2and prove that for all α > 0, G(α : n1,d, n1+ n2) ≠ ∅ if and only if G(α : n2,d, n1+ n2) ≠ ∅. For g = 2, we describe G(α : 2,d,k) for k > n.

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 (&gt; 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.

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