Stochastic Comparisons Between Coherent Systems with Active Redundancies Under Proportional Hazards and Reversed Hazards Models

2020 ◽  
Vol 28 (01) ◽  
pp. 2150007
Author(s):  
Maryam Kelkinnama
Keyword(s):  
Proportional Hazards ◽  
Sufficient Conditions ◽  
System Level ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Component Level ◽  
Lifetime Distributions ◽  
Hazards Model ◽  
System Improvement

This paper is concerned with the problem of stochastic comparisons between the lifetimes of two coherent systems with active redundancy. For this purpose, we consider both the active redundancy at the system level and the redundancy at the component level. We assume that the original components are identically distributed and possibly dependent. It is also assumed that for each component, there are [Formula: see text] redundant components with possibly different lifetime distributions which follow the proportional hazards (reversed hazards) model. Under some conditions on the domination function of the system, we compare the lifetimes of the systems based on majorization orders between the parameter vectors of the proportionality of the component lifetimes. We also give sufficient conditions under which adding more redundant components imply the system improvement.

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.

scholarly journals Stochastic Comparisons of Residual Lifetimes and Inactivity Times of Coherent Systems

2013 ◽  
Vol 50 (3) ◽  
pp. 848-860 ◽  
Author(s):  
Nitin Gupta
Keyword(s):  
Likelihood Ratio ◽  
Sufficient Conditions ◽  
Structure Functions ◽  
Coherent System ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Likelihood Ratio Ordering ◽  
Necessary And Sufficient ◽  
Residual Lifetimes

Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, for r-out-of-n systems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

Orderings of component level versus system level at active redundancies for coherent systems with dependent components

2021 ◽  
pp. 1-23
Author(s):  
Rongfang Yan ◽  
Junrui Wang ◽  
Bin Lu
Keyword(s):  
Hazard Rate ◽  
System Level ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Component Level ◽  
Comparison Results ◽  
Versus System ◽  
Level Versus ◽  
Theoretical Results ◽  
Complete Matching

This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.

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.

Stochastic Comparisons of Residual Lifetimes and Inactivity Times of Coherent Systems

2013 ◽  
Vol 50 (03) ◽  
pp. 848-860 ◽  
Author(s):  
Nitin Gupta
Keyword(s):  
Likelihood Ratio ◽  
Sufficient Conditions ◽  
Structure Functions ◽  
Coherent System ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Likelihood Ratio Ordering ◽  
Necessary And Sufficient ◽  
Residual Lifetimes

Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, forr-out-of-nsystems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

ON THE RESIDUAL AND PAST LIFETIMES OF COHERENT SYSTEMS UNDER RANDOM MONITORING

2020 ◽  
pp. 1-16
Author(s):  
Ebrahim Amini-Seresht ◽  
Maryam Kelkinnama ◽  
Yiying Zhang
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
System Structure ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Distortion Functions ◽  
Aging Properties ◽  
Observation Times ◽  
Theoretical Results ◽  
Residual Lifetimes

This paper discusses stochastic comparisons for the residual and past lifetimes of coherent systems with dependent and identically distributed (d.i.d.) components under random monitoring in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orders. Some stochastic comparisons results are also established on the residual lifetimes of coherent systems under random observation times when all of the components are alive at that time. Sufficient conditions are established in terms of the aging properties of the components and the distortion functions induced from the system structure and dependence among components lifetimes. Numerical examples are provided to illustrate the theoretical results as well.

scholarly journals Comparing lifetimes of coherent systems with dependent components operating in random environments

2019 ◽  
Vol 56 (3) ◽  
pp. 937-957
Author(s):  
Nil Kamal Hazra ◽  
Maxim Finkelstein
Keyword(s):  
Random Environment ◽  
Sufficient Conditions ◽  
The Other ◽  
Random Environments ◽  
Coherent System ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
The Impact ◽  
System Operating

AbstractWe study the impact of a random environment on lifetimes of coherent systems with dependent components. There are two combined sources of this dependence. One results from the dependence of the components of the coherent system operating in a deterministic environment and the other is due to dependence of components of the system sharing the same random environment. We provide different sets of sufficient conditions for the corresponding stochastic comparisons and consider various scenarios, namely, (i) two different (as a specific case, identical) coherent systems operate in the same random environment; (ii) two coherent systems operate in two different random environments; (iii) one of the coherent systems operates in a random environment and the other in a deterministic environment. Some examples are given to illustrate the proposed reasoning.

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.

scholarly journals Some new results on stochastic comparisons of coherent systems using signatures

2020 ◽  
Vol 57 (1) ◽  
pp. 156-173
Author(s):  
Ebrahim Amini-Seresht ◽  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Sufficient Conditions ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Numerical Examples ◽  
Distributed Components ◽  
Signature Vector ◽  
Theoretical Results ◽  
Independent And Identically Distributed

AbstractWe consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed component lifetimes. Some numerical examples are also provided to illustrate the theoretical results.

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