The optimal allocation of active redundancies to k-out-of-n systems with respect to hazard rate ordering

2012 ◽  
Vol 142 (7) ◽  
pp. 1878-1887 ◽  
Author(s):  
Weiyong Ding ◽  
Xiaohu Li
Keyword(s):  
Hazard Rate ◽  
Optimal Allocation ◽  
Hazard Rate Ordering

STOCHASTIC ARRANGEMENT INEQUALITIES FOR SOME SYSTEMS WITH HAZARD-RATE ORDERED COMPONENTS

1994 ◽  
Vol 01 (02) ◽  
pp. 185-196
Author(s):  
HAIJUN LI
Keyword(s):  
Hazard Rate ◽  
Optimal Allocation ◽  
Random Variables ◽  
Monotonicity Property ◽  
Hazard Rate Ordering ◽  
Parametrized Family

Using an arrangement monotonicity property of the parametrized family of hazard rate ordered random variables, and a bivariate characterization of the hazard rate ordering, we obtain some new stochastic arrangement inequalities for the random variables that are hazard rate ordered. Some applications of optimal allocation and assembly are also discussed.

Optimal allocation of a coherent system with statistical dependent subsystems

2021 ◽  
pp. 1-20
Author(s):  
Bin Lu ◽  
Jiandong Zhang ◽  
Rongfang Yan
Keyword(s):  
Hazard Rate ◽  
Optimal Allocation ◽  
Stochastic Order ◽  
Sufficient Conditions ◽  
Parallel Systems ◽  
Coherent System ◽  
Allocation Policy ◽  
Usual Stochastic Order ◽  
Series Systems ◽  
Parallel Series

Abstract This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

Dynamic multivariate mean residual life functions

1991 ◽  
Vol 28 (03) ◽  
pp. 613-629 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Partial Ordering ◽  
Mean Residual Life ◽  
Positive Dependence ◽  
Basic Properties ◽  
Rate Functions ◽  
Hazard Rate Ordering ◽  
Weak Notion

In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied. A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given. Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.

scholarly journals CORRECTION TO “DEPENDENCE, DISPERSIVENESS, AND MULTIVARIATE HAZARD RATE ORDERING”

2006 ◽  
Vol 20 (2) ◽  
pp. 381-381
Author(s):  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Opposite Direction ◽  
Hazard Rate ◽  
Hazard Rate Ordering

In the article published last year, three inequalities should be in the opposite direction.

On allocation of spares at component level versus system level

1997 ◽  
Vol 34 (01) ◽  
pp. 283-287 ◽  
Author(s):  
Harshinder Singh ◽  
R. S. Singh
Keyword(s):  
Survival Analysis ◽  
Hazard Rate ◽  
System Level ◽  
Component Level ◽  
Design Engineers ◽  
Versus System ◽  
Level Versus ◽  
Life Distributions ◽  
Likelihood Ratio Ordering ◽  
Hazard Rate Ordering

Design engineers are well aware that a system where active spare allocation is made at the component level has a lifetime stochastically larger than the corresponding system where active spare allocation is made at the system level. In view of the importance of hazard rate ordering in reliability and survival analysis, Boland and El-Neweihi (1995) recently investigated this principle in hazard rate ordering and demonstrated that it does not hold in general. They showed that for a 2-out-of-n system with independent and identical components and spares, active spare allocation at the component level is superior to active spare allocation at the system level. They conjectured that such a principle holds in general for a k-out-of-n system when components and spares are independent and identical. We prove that for a k-out-of-n system where components and spares have independent and identical life distributions active spare allocation at the component level is superior to active spare allocation at the system level in likelihood ratio ordering. This is stronger than hazard rate ordering, thus establishing the conjecture of Boland and El-Neweihi (1995).

scholarly journals Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
S. Ramasubramanian ◽  
P. Mahendran
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Mean Residual Life ◽  
Mean And Variance ◽  
The Mean ◽  
Hazard Rate Ordering ◽  
Fuzzy Random

L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variablesXandY.

scholarly journals DEPENDENCE, DISPERSIVENESS, AND MULTIVARIATE HAZARD RATE ORDERING

2005 ◽  
Vol 19 (4) ◽  
pp. 427-446 ◽  
Author(s):  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Multivariate Analysis ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Vectors ◽  
Positive Dependence ◽  
Marginal Distributions ◽  
Dispersive Ordering ◽  
Hazard Rate Ordering

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of two upper orthant dispersive ordered random vectors are also dispersive ordered. Examples and applications are given.

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