scholarly journals Monomial ideals and the Scarf complex for coherent systems in reliability theory

2004 ◽  
Vol 32 (3) ◽  
pp. 1289-1311 ◽  
Author(s):  
Beatrice Giglio ◽  
Henry P. Wynn
Keyword(s):  
Reliability Theory ◽  
Monomial Ideals ◽  
Coherent Systems

More on optimal allocation of components in coherent systems

1996 ◽  
Vol 33 (02) ◽  
pp. 548-556 ◽  
Author(s):  
Fan C. Meng
Keyword(s):  
System Reliability ◽  
Binary Systems ◽  
Optimal Allocation ◽  
Reliability Theory ◽  
Parallel System ◽  
System Level ◽  
Coherent Systems ◽  
Component Level ◽  
Multistate Systems ◽  
Permutation Equivalent

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

Modelling dependence in simple and indirect majority systems

1989 ◽  
Vol 26 (1) ◽  
pp. 81-88 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Decision Theory ◽  
Majority Rule ◽  
Reliability Theory ◽  
Correct Decision ◽  
Coherent Systems ◽  
Monotonicity Results ◽  
Do So

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.

scholarly journals Hazard rate ordering of order statistics and systems

2006 ◽  
Vol 43 (02) ◽  
pp. 391-408 ◽  
Author(s):  
Jorge Navarro ◽  
Moshe Shaked
Keyword(s):  
Order Statistics ◽  
Random Vector ◽  
Hazard Rate ◽  
Rate Function ◽  
Reliability Theory ◽  
Hazard Rate Function ◽  
Coherent Systems ◽  
Hazard Rate Order ◽  
Limiting Behaviour ◽  
Hazard Rate Ordering

LetX= (X1,X2, …,Xn) be an exchangeable random vector, and writeX(1:i)= min{X1,X2, …,Xi}, 1 ≤i≤n. In this paper we obtain conditions under whichX(1:i)decreases iniin the hazard rate order. A result involving more general (that is, not necessarily exchangeable) random vectors is also derived. These results are applied to obtain the limiting behaviour of the hazard rate function of the lifetimes of various coherent systems in reliability theory. The notions of the Samaniego signatures and the minimal signatures of such systems are extensively used in the paper. An interesting relationship between these two signatures is obtained. The results are illustrated in a series of examples.

scholarly journals Hazard rate ordering of order statistics and systems

2006 ◽  
Vol 43 (2) ◽  
pp. 391-408 ◽  
Author(s):  
Jorge Navarro ◽  
Moshe Shaked
Keyword(s):  
Order Statistics ◽  
Random Vector ◽  
Hazard Rate ◽  
Rate Function ◽  
Reliability Theory ◽  
Hazard Rate Function ◽  
Coherent Systems ◽  
Hazard Rate Order ◽  
Limiting Behaviour ◽  
Hazard Rate Ordering

Let X = (X1, X2, …, Xn) be an exchangeable random vector, and write X(1:i) = min{X1, X2, …, Xi}, 1 ≤ i ≤ n. In this paper we obtain conditions under which X(1:i) decreases in i in the hazard rate order. A result involving more general (that is, not necessarily exchangeable) random vectors is also derived. These results are applied to obtain the limiting behaviour of the hazard rate function of the lifetimes of various coherent systems in reliability theory. The notions of the Samaniego signatures and the minimal signatures of such systems are extensively used in the paper. An interesting relationship between these two signatures is obtained. The results are illustrated in a series of examples.

A CUMULATIVE RESIDUAL INACCURACY MEASURE FOR COHERENT SYSTEMS AT COMPONENT LEVEL AND UNDER NONHOMOGENEOUS POISSON PROCESSES

2020 ◽  
pp. 1-26
Author(s):  
Vanderlei da Costa Bueno ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Reliability Theory ◽  
Poisson Processes ◽  
Residual Entropy ◽  
Coherent Systems ◽  
Component Level ◽  
Martingale Approach ◽  
Information Measures ◽  
Cumulative Residual Entropy ◽  
Nonhomogeneous Poisson Processes ◽  
Cumulative Residual

Inaccuracy and information measures based on cumulative residual entropy are quite useful and have attracted considerable attention in many fields including reliability theory. Using a point process martingale approach and a compensator version of Kumar and Taneja's generalized inaccuracy measure of two nonnegative continuous random variables, we define here an inaccuracy measure between two coherent systems when the lifetimes of their common components are observed. We then extend the results to the situation when the components in the systems are subject to failure according to a double stochastic Poisson process.

More on optimal allocation of components in coherent systems

1996 ◽  
Vol 33 (2) ◽  
pp. 548-556 ◽  
Author(s):  
Fan C. Meng
Keyword(s):  
System Reliability ◽  
Binary Systems ◽  
Optimal Allocation ◽  
Reliability Theory ◽  
Parallel System ◽  
System Level ◽  
Coherent Systems ◽  
Component Level ◽  
Multistate Systems ◽  
Permutation Equivalent

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

Coherent Systems in Profust Reliability Theory

1995 ◽  
pp. 81-94 ◽  
Author(s):  
Kai-Yuan Cai ◽  
Chuan-Yuan Wen ◽  
Ming-Lian Zhang
Keyword(s):  
Reliability Theory ◽  
Coherent Systems

Modelling dependence in simple and indirect majority systems

1989 ◽  
Vol 26 (01) ◽  
pp. 81-88 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Decision Theory ◽  
Majority Rule ◽  
Reliability Theory ◽  
Correct Decision ◽  
Coherent Systems ◽  
Monotonicity Results ◽  
Do So

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.

Sign in / Sign up

Export Citation Format

Share Document