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.

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.

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.

On inactivity times of failed components of coherent system under double monitoring

2021 ◽  
pp. 1-18
Author(s):  
Zhouxia Guo ◽  
Jiandong Zhang ◽  
Rongfang Yan
Keyword(s):  
Sufficient Conditions ◽  
Reliability Function ◽  
Coherent System ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Stochastic Behavior ◽  
Numerical Examples ◽  
Comparison Results ◽  
Aging Properties ◽  
Theoretical Results

Abstract This article discusses the stochastic behavior and reliability properties for the inactivity times of failed components in coherent systems under double monitoring. A mixture representation of reliability function is obtained for the inactivity times of failed components, and some stochastic comparison results are also established. Furthermore, some sufficient conditions are developed in terms of the aging properties of the inactivity times of failed components. Finally, some numerical examples are presented to illustrate the theoretical results.

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.

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.

Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics

2021 ◽  
pp. 1-20
Author(s):  
Mahdi Alimohammadi ◽  
Maryam Esna-Ashari ◽  
Jorge Navarro
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Stochastic Comparisons ◽  
Sequential Order Statistics ◽  
Progressive Type ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$ -spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$ -record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

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.

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.

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.

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