On the shape of the mean residual lifetime function

2002 ◽  
Vol 18 (2) ◽  
pp. 135-146 ◽  
Author(s):  
M. S. Finkelstein
Keyword(s):  
Residual Lifetime ◽  
Mean Residual Lifetime ◽  
The Mean

scholarly journals On the nonoptimality of the foreground-background discipline for IMRL service times

2006 ◽  
Vol 43 (02) ◽  
pp. 523-534
Author(s):  
S. Aalto ◽  
U. Ayesta
Keyword(s):  
Hazard Rate ◽  
Residual Lifetime ◽  
Processor Sharing ◽  
Counter Example ◽  
Mean Delay ◽  
Mean Residual Lifetime ◽  
Service Disciplines ◽  
The Mean ◽  
Service Times ◽  
The One

It is known that for decreasing hazard rate (DHR) service times the foreground-background discipline (FB) minimizes the mean delay in the M/G/1 queue among all work-conserving and nonanticipating service disciplines. It is believed that a similar result is valid for increasing mean residual lifetime (IMRL) service times. However, on the one hand, we point out a flaw in an earlier proof of the latter result and construct a counter-example that demonstrates that FB is not necessarily optimal within class IMRL. On the other hand, we prove that the mean delay for FB is smaller than that of the processor-sharing discipline within class IMRL, giving a weaker version of an earlier hypothesis.

Characterization of matrix probability distributions by mean residual lifetime

1986 ◽  
Vol 100 (3) ◽  
pp. 583-589
Author(s):  
P. E. Jupp
Keyword(s):  
Symmetric Matrix ◽  
Probability Distributions ◽  
Random Variable ◽  
Residual Lifetime ◽  
Regularity Conditions ◽  
Mean Residual Lifetime ◽  
The Mean ◽  
Image Position ◽  
Vector Valued

The mean residual lifetime of a real-valued random variable X is the function e defined byOne of the more important properties of the mean residual lifetime function is that it determines the distribution of X. See, for example, Swartz [10]. References to related characterizations are given by Galambos and Kotz [3], pages 30–35. It was established by Jupp and Mardia[6] that this property holds also for vector-valued X. As (1·1) makes sense if X is a random symmetric matrix, it is natural to ask whether the property holds in this case also. The purpose of this note is to show that, under certain regularity conditions, the distributions of such matrices are indeed determined by their mean residual lifetimes.

scholarly journals On the nonoptimality of the foreground-background discipline for IMRL service times

2006 ◽  
Vol 43 (2) ◽  
pp. 523-534 ◽  
Author(s):  
S. Aalto ◽  
U. Ayesta
Keyword(s):  
Hazard Rate ◽  
Residual Lifetime ◽  
Processor Sharing ◽  
Counter Example ◽  
Mean Delay ◽  
Mean Residual Lifetime ◽  
Service Disciplines ◽  
The Mean ◽  
Service Times ◽  
The One

It is known that for decreasing hazard rate (DHR) service times the foreground-background discipline (FB) minimizes the mean delay in the M/G/1 queue among all work-conserving and nonanticipating service disciplines. It is believed that a similar result is valid for increasing mean residual lifetime (IMRL) service times. However, on the one hand, we point out a flaw in an earlier proof of the latter result and construct a counter-example that demonstrates that FB is not necessarily optimal within class IMRL. On the other hand, we prove that the mean delay for FB is smaller than that of the processor-sharing discipline within class IMRL, giving a weaker version of an earlier hypothesis.

scholarly journals Mean Residual Lifetimes of Consecutive-k-out-of-n Systems

2007 ◽  
Vol 44 (1) ◽  
pp. 82-98 ◽  
Author(s):  
Jorge Navarro ◽  
Serkan Eryilmaz
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Parallel Systems ◽  
Residual Lifetime ◽  
Series System ◽  
Likelihood Ratio Order ◽  
Mean Residual Lifetime ◽  
The Mean ◽  
Residual Lifetimes ◽  
Independent And Identically Distributed

In this paper we study reliability properties of consecutive-k-out-of-n systems with exchangeable components. For 2k ≦ n, we show that the reliability functions of these systems can be written as negative mixtures (i.e. mixtures with some negative weights) of two series (or parallel) systems. Some monotonicity and asymptotic properties for the mean residual lifetime function are obtained and some ordering properties between these systems are established. We prove that, under some assumptions, the mean residual lifetime function of the consecutive-k-out-of-n: G system (i.e. a system that functions if and only if at least k consecutive components function) is asymptotically equivalent to that of a series system with k components. When the components are independent and identically distributed, we show that consecutive-k-out-of-n systems are ordered in the likelihood ratio order and, hence, in the mean residual lifetime order, for 2k ≦ n. However, we show that this is not necessarily true when the components are dependent.

scholarly journals Mean Residual Lifetimes of Consecutive-k-out-of-n Systems

2007 ◽  
Vol 44 (01) ◽  
pp. 82-98 ◽  
Author(s):  
Jorge Navarro ◽  
Serkan Eryilmaz
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Parallel Systems ◽  
Residual Lifetime ◽  
Series System ◽  
Likelihood Ratio Order ◽  
Mean Residual Lifetime ◽  
The Mean ◽  
Residual Lifetimes ◽  
Independent And Identically Distributed

In this paper we study reliability properties of consecutive-k-out-of-n systems with exchangeable components. For 2k ≦ n, we show that the reliability functions of these systems can be written as negative mixtures (i.e. mixtures with some negative weights) of two series (or parallel) systems. Some monotonicity and asymptotic properties for the mean residual lifetime function are obtained and some ordering properties between these systems are established. We prove that, under some assumptions, the mean residual lifetime function of the consecutive-k-out-of-n: G system (i.e. a system that functions if and only if at least k consecutive components function) is asymptotically equivalent to that of a series system with k components. When the components are independent and identically distributed, we show that consecutive-k-out-of-n systems are ordered in the likelihood ratio order and, hence, in the mean residual lifetime order, for 2k ≦ n. However, we show that this is not necessarily true when the components are dependent.

On the mean residual lifetime of consecutive k-out-of-n systems

Test ◽  
2011 ◽  
Vol 21 (1) ◽  
pp. 93-115 ◽  
Author(s):  
E. T. Salehi ◽  
M. Asadi ◽  
S. Eryılmaz
Keyword(s):  
Residual Lifetime ◽  
Mean Residual Lifetime ◽  
The Mean
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