scholarly journals On the Lifetime and Signature of Constrained (k, d)-out-of-n: F Reliability Systems

2020 ◽  
Vol 6 (1) ◽  
pp. 66-78 ◽  
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Multivariate Distribution ◽  
Residual Lifetime ◽  
Reliability Study ◽  
Conditional Mean ◽  
Mean Residual Lifetime ◽  
Signature Vector ◽  
Reliability Systems

In the present paper we carry out a reliability study of the constrained (k, d)-out-of-n: F systems with exchangeable components. The signature vector is computed by the aid of the proposed algorithm. In addition, explicit signature-based expressions for the corresponding mean residual lifetime and the conditional mean residual lifetime of the aforementioned reliability system are also provided. For illustration purposes, a well-known multivariate distribution for modelling the lifetimes of the components of the constrained (k, d)-out-of-n: F structure is considered.

scholarly journals On the Consecutive k1 and k2-out-of-n Reliability Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 630
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Generating Function ◽  
Recurrence Relations ◽  
Reliability Function ◽  
Numerical Results ◽  
Reliability Study ◽  
Distributed Components ◽  
Signature Vector ◽  
Reliability Systems ◽  
Independent And Identically Distributed

In this paper we carry out a reliability study of the consecutive-k1 and k2-out-of-n systems with independent and identically distributed components ordered in a line. More precisely, we obtain the generating function of the structure’s reliability, while recurrence relations for determining its signature vector and reliability function are also provided. For illustration purposes, some numerical results and figures are presented and several concluding remarks are deduced.

scholarly journals On estimating optimal regime for treatment initiation time based on restricted mean residual lifetime

Biometrics ◽  
2021 ◽  
Author(s):  
Xin Chen ◽  
Rui Song ◽  
Jiajia Zhang ◽  
Swann Arp Adams ◽  
Liuquan Sun ◽  
...  
Keyword(s):  
Treatment Initiation ◽  
Residual Lifetime ◽  
Initiation Time ◽  
Optimal Regime ◽  
Mean Residual Lifetime

scholarly journals A Dynamic Failure Time Degradation-Based Model

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1532
Author(s):  
Abdulhakim A. Albabtain ◽  
Mansour Shrahili ◽  
Lolwa Alshagrawi ◽  
Mohamed Kayid
Keyword(s):  
Hazard Rate ◽  
Failure Time ◽  
Degradation Process ◽  
Residual Lifetime ◽  
Time To Failure ◽  
Lifetime Distributions ◽  
Mean Residual Lifetime ◽  
Aging Properties ◽  
Degradation Models ◽  
Characterization Property

A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established.

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.

Estimation of Two Ordered Mean Residual Lifetime Functions

Biometrics ◽  
1993 ◽  
Vol 49 (2) ◽  
pp. 409 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Residual Lifetime ◽  
Mean Residual Lifetime
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