Stochastic comparisons of coherent systems under different random environments

2018 ◽  
Vol 55 (2) ◽  
pp. 459-472 ◽  
Author(s):  
Ebrahim Amini-Seresht ◽  
Yiying Zhang ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
Random Environments ◽  
Reliability Engineering ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Numerical Examples ◽  
Reversed Hazard Rate ◽  
Collaborative Environment ◽  
Theoretical Results

Abstract For many practical situations in reliability engineering, components in the system are usually dependent since they generally work in a collaborative environment. In this paper we build sufficient conditions for comparing two coherent systems under different random environments in the sense of the usual stochastic, hazard rate, reversed hazard rate, and likelihood ratio orders. Applications and numerical examples are provided to illustrate all the theoretical results established here.

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.

COMPARISONS OF SAMPLE RANGES ARISING FROM MULTIPLE-OUTLIER MODELS: IN MEMORY OF MOSHE SHAKED

2017 ◽  
Vol 33 (1) ◽  
pp. 28-49
Author(s):  
Narayanaswamy Balakrishnan ◽  
Jianbin Chen ◽  
Yiying Zhang ◽  
Peng Zhao
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Sufficient Conditions ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Numerical Examples ◽  
Reversed Hazard Rate ◽  
Usual Stochastic Order

In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.

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 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.

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.

COMPARISONS ON LARGEST ORDER STATISTICS FROM HETEROGENEOUS GAMMA SAMPLES

2020 ◽  
pp. 1-20
Author(s):  
Ting Zhang ◽  
Yiying Zhang ◽  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Hazard Rate ◽  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Shape Parameters ◽  
Reliability Engineering ◽  
Stochastic Comparisons ◽  
Maximum Order ◽  
Scale Parameters ◽  
Hazard Rate Ordering

This paper deals with stochastic comparisons of the largest order statistics arising from two sets of independent and heterogeneous gamma samples. It is shown that the weak supermajorization order between the vectors of scale parameters together with the weak submajorization order between the vectors of shape parameters imply the reversed hazard rate ordering between the corresponding maximum order statistics. We also establish sufficient conditions of the usual stochastic ordering in terms of the p-larger order between the vectors of scale parameters and the weak submajorization order between the vectors of shape parameters. Numerical examples and applications in auction theory and reliability engineering are provided to illustrate these results.

ACTIVE REDUNDANCY ALLOCATION FOR COHERENT SYSTEMS WITH INDEPENDENT AND HETEROGENEOUS COMPONENTS

2018 ◽  
Vol 34 (1) ◽  
pp. 72-91 ◽  
Author(s):  
Rui Fang ◽  
Xiaohu Li
Keyword(s):  
Sufficient Conditions ◽  
Coherent Systems ◽  
Minimal Path ◽  
Redundancy Allocation ◽  
Numerical Examples ◽  
Minimal Cut Sets ◽  
Minimal Cut ◽  
Minimal Path Sets ◽  
Theoretical Results

This paper studies the allocation of active redundancies to coherent systems on the context that the base and redundancy components have mutual independent lifetimes. For systems with two symmetric components and systems with one component's minimal cut sets (minimal path sets) covering those of another, we derive sufficient conditions to compare the resultant system lifetimes. Some numerical examples are also presented to illustrate the theoretical results.

Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fatih Kızılaslan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Design Methodology ◽  
Parallel Systems ◽  
Parallel System ◽  
Series System ◽  
Stochastic Comparisons ◽  
Content Type ◽  
Reversed Hazard Rate ◽  
The Relationship

PurposeThe purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.Design/methodology/approachThe obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.FindingsThe reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.Originality/valueTo the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

Sign in / Sign up

Export Citation Format

Share Document