On the mean residual life order of convolutions of independent uniform random variables

The concept of mean residual life plays an important role in reliability and life testing. In this paper, we introduce and study a new stochastic order called proportional mean residual life order. Several characterizations and preservation properties of the new order under some reliability operations are discussed. As a consequence, a new class of life distributions is introduced on the basis of the anti-star-shaped property of the mean residual life function. We study some reliability properties and some characterizations of this class and provide some examples of interest in reliability.

Download Full-text

Preservation of the mean residual life order for coherent and mixed systems

Journal of Applied Probability ◽

10.1017/jpr.2019.11 ◽

2019 ◽

Vol 56 (01) ◽

pp. 153-173 ◽

Cited By ~ 2

Author(s):

Bo H. Lindqvist ◽

Francisco J. Samaniego ◽

Nana Wang

Keyword(s):

Residual Life ◽

Stochastic Order ◽

Mean Residual Life ◽

Coherent System ◽

Hazard Rate Order ◽

Stochastic Orderings ◽

Mean Residual Life Order ◽

The Mean ◽

Point Of Departure ◽

Mixed Systems

AbstractThe signature of a coherent system has been studied extensively in the recent literature. Signatures are particularly useful in the comparison of coherent or mixed systems under a variety of stochastic orderings. Also, certain signature-based closure and preservation theorems have been established. For example, it is now well known that certain stochastic orderings are preserved from signatures to system lifetimes when components have independent and identical distributions. This applies to the likelihood ratio order, the hazard rate order, and the stochastic order. The point of departure of the present paper is the question of whether or not a similar preservation result will hold for the mean residual life order. A counterexample is provided which shows that the answer is negative. Classes of distributions for the component lifetimes for which the latter implication holds are then derived. Connections to the theory of order statistics are also considered.

Download Full-text

SOME NEW RESULTS ON ORDERING OF SIMPLE SPACINGS OF GENERALIZED ORDER STATISTICS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964810000252 ◽

2010 ◽

Vol 25 (1) ◽

pp. 71-81 ◽

Cited By ~ 5

Author(s):

Hongmei Xie ◽

Weiwei Zhuang

Keyword(s):

Order Statistics ◽

Residual Life ◽

Random Variables ◽

Generalized Order Statistics ◽

Mean Residual Life ◽

Unified Approach ◽

Stochastic Comparisons ◽

The Mean ◽

Generalized Order

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to establish several stochastic comparisons of simple spacings in the mean residual life and the excess wealth orders under the more general assumptions on the parameters of the models.

Download Full-text

Comparisons in the mean residual life order of coherent systems with identically distributed components

Applied Stochastic Models in Business and Industry ◽

10.1002/asmb.2121 ◽

2015 ◽

Vol 32 (1) ◽

pp. 33-47 ◽

Cited By ~ 20

Author(s):

Jorge Navarro ◽

M. Carmen Gomis

Keyword(s):

Residual Life ◽

Mean Residual Life ◽

Coherent Systems ◽

Distributed Components ◽

Mean Residual Life Order ◽

The Mean

Download Full-text

ORDERING CONVOLUTIONS OF HETEROGENEOUS EXPONENTIAL AND GEOMETRIC DISTRIBUTIONS REVISITED

Probability in the Engineering and Informational Sciences ◽

10.1017/s026996481000001x ◽

2010 ◽

Vol 24 (3) ◽

pp. 329-348 ◽

Cited By ~ 7

Author(s):

Tiantian Mao ◽

Taizhong Hu ◽

Peng Zhao

Keyword(s):

Hazard Rate ◽

Residual Life ◽

Sufficient Conditions ◽

Random Variables ◽

Mean Residual Life ◽

Reversed Hazard Rate ◽

Exponential Random Variables ◽

The Mean ◽

Geometric Variables ◽

Fail Safe

Let Sn(a1, …, an) be the sum of n independent exponential random variables with respective hazard rates a1, …, an or the sum of n independent geometric random variables with respective parameters a1, …, an. In this article, we investigate sufficient conditions on parameter vectors (a1, …, an) and $(a_{1}^{\ast},\ldots,a_{n}^{\ast})$ under which Sn(a1, …, an) and $S_{n}(a_{1}^{\ast},\ldots,a_{n}^{\ast})$ are ordered in terms of the increasing convex and the reversed hazard rate orders for both exponential and geometric random variables and in terms of the mean residual life order for geometric variables. For the bivariate case, all of these sufficient conditions are also necessary. These characterizations are used to compare fail-safe systems with heterogeneous exponential components in the sense of the increasing convex and the reversed hazard rate orders. The main results complement several known ones in the literature.

Download Full-text