A Study of the Role of Modules in the Failure of Systems

1991 ◽  
Vol 5 (2) ◽  
pp. 215-227 ◽  
Author(s):  
Emad El Neweihi ◽  
Jayaram Sethuraman
Keyword(s):  
Optimal Allocation ◽  
System Failure ◽  
Coherent Systems ◽  
Expected Number ◽  
Number Of Components ◽  
Monotonicity Properties

Since the introduction of the concept of coherent systems and the description of the reliability of such systems in terms of the reliabilities of the components, the concept of importance of a component has created a new and fruitful area of research. Two distinct concepts of importance can be found in the literature. We take the view that the importance of a component or a module that is part of a system can be derived directly from the role of the component or the module in the failure of the system. Here again, it is possible that there will be several definitions of role. In this paper we define the role of a module (or component) to be the probability that the module is among all the modules (or components) that failed at the time of system failure. The role of a module depends on the structure of the system in terms of the modules, the structure of the module in terms of its components and the distribution of lifetimes of the components. In this paper we study the role of a module under several structures and distributions for lifetimes. We establish various monotonicity properties and indicate applications of these properties to optimal allocation. Another quantity that describes the nature of the components in sustaining the system is the number of components that fail at the time of the failure of the system. We establish monotonicity properties for the expected number of failed components and also indicate applications to optimal allocation.

The Role of a Group of Modules in the Failure of Systems

1994 ◽  
Vol 8 (1) ◽  
pp. 89-101
Author(s):  
A. M. Abouammoh ◽  
Emad El-Neweihi ◽  
Jayaram Sethuraman
Keyword(s):  
Random Variable ◽  
Expected Value ◽  
Second Order ◽  
System Failure ◽  
Monotonicity Properties ◽  
Multistate Systems

Consider a system consisting of a number of modules. The probability that a particular module is among the ones that have already failed by the time of system failure can be used as a measure of the importance of that module. In El-Neweihi and Sethuraman [6], this probability was called the role of a module in the failure of a system and its properties were developed. In this article we propose the number of failed modules from among a particular subgroup of modules as the basis for measuring the role of that subgroup of modules. We study some monotonicity properties of the distribution of that random variable, in some second order r-out-of-k systems. We illustrate the possible extensions of these results to multistate systems. Yet another measure of the role of a particular subgroup of modules can be based on the number of failed components from this subgroup by the time of system failure. We derive some monotonicity properties of the expected value of the number of such failed components.

Optimal allocation of relevations in coherent systems

2021 ◽  
Vol 58 (4) ◽  
pp. 1152-1169
Author(s):  
Rongfang Yan ◽  
Jiandong Zhang ◽  
Yiying Zhang
Keyword(s):  
Optimal Allocation ◽  
Necessary Conditions ◽  
Stochastic Order ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Usual Stochastic Order ◽  
Special Cases ◽  
Sufficient And Necessary Conditions ◽  
Allocation Strategies

AbstractIn this paper we study the allocation problem of relevations in coherent systems. The optimal allocation strategies are obtained by implementing stochastic comparisons of different policies according to the usual stochastic order and the hazard rate order. As special cases of relevations, the load-sharing and minimal repair policies are further investigated. Sufficient (and necessary) conditions are established for various stochastic orderings. Numerical examples are also presented as illustrations.

Performance evaluation of alternate policies on reservoir system operation

1986 ◽  
Vol 13 (2) ◽  
pp. 203-212 ◽  
Author(s):  
J. R. Weeraratne ◽  
Lloyd Logan ◽  
T. E. Unny
Keyword(s):  
River System ◽  
Primary Objective ◽  
Performance Criteria ◽  
Decision Making Process ◽  
System Failure ◽  
System Operation ◽  
System Vulnerability ◽  
Operational Policies ◽  
System Robustness

This paper discusses within the context of the Grand River system operation the application of the three performance criteria introduced earlier by T. Hashimoto, D. P. Loucks, and J. R. Stedinger. These criteria evaluate the performance characteristic in respect to system failure, system recovery, and system vulnerability with regard to extreme (costly) failures for alternative operational policies. System robustness, also discussed by Hashimoto and co-workers, is used to measure the economic flexibility of system operation to adapt to uncertainties of future demand. The primary objective of the presentation made herein is to establish the role of these criteria in a decision-making process in the operation of the system.

Optimal Allocation of Components in k-out-of-R Parallel Modules Systems

1994 ◽  
Vol 8 (3) ◽  
pp. 435-441 ◽  
Author(s):  
Fan Chin Meng
Keyword(s):  
System Reliability ◽  
Optimal Allocation ◽  
Parallel Systems ◽  
Coherent Systems ◽  
Special Case

In this note using the notion of node criticality in Boland, Proschan, and Tong [2] and modular decompositions of coherent systems, we obtain algorithms and guidelines for allocating components in a k-out-of-R parallel modules system to maximize the system reliability. An illustrative example is given to compare a special case of our results with the previous result for series-parallel systems due to El-Neweihi, Proschan, and Sethuraman [5].

Initial and final behaviour of failure rate functions for mixtures and systems

2003 ◽  
Vol 40 (03) ◽  
pp. 721-740 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Rate Function ◽  
Coherent Systems ◽  
Failure Rate Function ◽  
Rate Functions ◽  
Limiting Behaviour

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

The Pathophysiology of Multi-System Organ Failure in the Trauma Patient

1990 ◽  
Vol 1 (3) ◽  
pp. 465-476 ◽  
Author(s):  
Ann N. Hotter
Keyword(s):  
Organ Failure ◽  
Care Setting ◽  
Inflammatory Factors ◽  
System Failure ◽  
Organ Systems ◽  
Organ System Failure ◽  
Trauma Mortality ◽  
Physiologic Effect ◽  
System Organ

Multiple trauma mortality in the critical care setting most often occurs as a result of multi-system organ failure (MSOF). Mortality rates increase exponentially as successive organ systems fail. Although the role of shock in determining patient outcome has been extensively investigated, inflammatory factors and sepsis are becoming increasingly implicated in the development of MSOF. The physiologic effect of these factors on individual organ systems is explained. Signs, symptoms, and key criteria for determining organ system failure also are presented to assist the nurse in recognition and prevention

scholarly journals Risk Premia and the Real Effects of Money

2020 ◽  
Vol 110 (7) ◽  
pp. 1995-2040 ◽  
Author(s):  
Sebastian Di Tella
Keyword(s):  
Interest Rates ◽  
Risk Premium ◽  
Risk Sharing ◽  
Optimal Allocation ◽  
Price Theory ◽  
The Real ◽  
Friedman Rule ◽  
Real Effects ◽  
Tax Subsidy

This paper proposes a flexible-price theory of the role of money in an economy with incomplete idiosyncratic risk sharing. When the risk premium goes up, money provides a safe store of value that prevents interest rates from falling, reducing investment. Investment is too high during booms when risk is low, and too low during slumps when risk is high. Monetary policy cannot correct this: money is superneutral and Ricardian equivalence holds. The optimal allocation requires the Friedman rule and a tax/subsidy on capital. The real effects of money survive even in the cashless limit. (JEL E32, E41, E43, E44, E52)

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