Multivariate hazard rates and stochastic ordering

1987 ◽  
Vol 19 (1) ◽  
pp. 123-137 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Stochastic Ordering ◽  
Load Sharing ◽  
Hazard Rates ◽  
Imperfect Repair

Properties of the conditional hazard rates of X1, · ··, Xn and Y1, · ··, Yn, which imply (X1, · ··, Xn) (Y1, · ··, Yn), are found. These are used to find conditions on the hazard rates of T = (T1, · ··, Tn) which ensure that T has the MIHR | property of Arjas (1981a) and the ‘weakened by failure’ property of Arjas and Norros (1984). Applications for load-sharing model and multivariate imperfect repair are given.

Multivariate hazard rates and stochastic ordering

1987 ◽  
Vol 19 (01) ◽  
pp. 123-137 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Stochastic Ordering ◽  
Load Sharing ◽  
Hazard Rates ◽  
Simple Property ◽  
Imperfect Repair

Properties of the conditional hazard rates of X 1, · ··, Xn and Y 1, · ··, Yn, which imply (X 1, · ··, Xn ) (Y 1, · ··, Yn ), are found. These are used to find conditions on the hazard rates of T = (T 1, · ··, Tn ) which ensure that T has the MIHR | property of Arjas (1981a) and the ‘weakened by failure’ property of Arjas and Norros (1984). Applications for load-sharing model and multivariate imperfect repair are given.

Multivariate conditional hazard rates and the MIFRA and MIFR properties

1988 ◽  
Vol 25 (01) ◽  
pp. 150-168 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Load Sharing ◽  
Hazard Rates ◽  
Reliability Model ◽  
Increasing Failure Rate ◽  
Imperfect Repair ◽  
The Relationship

If T = (T 1, · ··, Tn ) is a vector of random lifetimes then its distribution can be determined by a set λof multivariate conditional hazard rates. In this paper, sufficient conditions on λare found which imply that T is Block–Savits MIFRA (multivariate increasing failure rate average) or Savits MIFR (multivariate increasing failure rate). Applications for a multivariate reliability model of Ross and for load-sharing models are given. The relationship between Shaked and Shanthikumar model of multivariate imperfect repair and the MIFRA property is also discussed.

Multivariate conditional hazard rates and the MIFRA and MIFR properties

1988 ◽  
Vol 25 (1) ◽  
pp. 150-168 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Load Sharing ◽  
Hazard Rates ◽  
Reliability Model ◽  
Increasing Failure Rate ◽  
Imperfect Repair ◽  
The Relationship

If T = (T1, · ··, Tn) is a vector of random lifetimes then its distribution can be determined by a set λof multivariate conditional hazard rates. In this paper, sufficient conditions on λare found which imply that T is Block–Savits MIFRA (multivariate increasing failure rate average) or Savits MIFR (multivariate increasing failure rate). Applications for a multivariate reliability model of Ross and for load-sharing models are given. The relationship between Shaked and Shanthikumar model of multivariate imperfect repair and the MIFRA property is also discussed.

Load-Sharing Reliability Models with Different Component Sensitivities to Other Components’ Working States

2021 ◽  
Vol 53 (1) ◽  
pp. 107-132
Author(s):  
Tomasz Rychlik ◽  
Fabio Spizzichino
Keyword(s):  
Order Statistics ◽  
Load Sharing ◽  
Single Component ◽  
Generalized Order Statistics ◽  
Hazard Rates ◽  
System Operation ◽  
Reliability Models ◽  
Mixtures Of Distributions ◽  
Failure Times ◽  
Generalized Order

AbstractWe study the distributions of component and system lifetimes under the time-homogeneous load-sharing model, where the multivariate conditional hazard rates of working components depend only on the set of failed components, and not on their failure moments or the time elapsed from the start of system operation. Then we analyze its time-heterogeneous extension, in which the distributions of consecutive failure times, single component lifetimes, and system lifetimes coincide with mixtures of distributions of generalized order statistics. Finally we focus on some specific forms of the time-nonhomogeneous load-sharing model.

scholarly journals Further Results on the Proportional Vitalities Model

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1201
Author(s):  
Mohamed Kayid
Keyword(s):  
Growth Parameter ◽  
Stochastic Ordering ◽  
Survival Models ◽  
Hazard Rates ◽  
Time Varying ◽  
Proportional Hazard ◽  
Model Potentials ◽  
Dynamic Version

In contrast to many survival models such as proportional hazard rates and proportional mean residual lives, the proportional vitalities model has also been introduced in the literature. In this paper, further stochastic ordering properties of a dynamic version of the model with a random vitality growth parameter are investigated. Examples are presented to illustrate different established properties of the model. Potentials for inference about the parameters in proportional vitalities model with possibly time-varying effects are also argued and discussed.

A STUDY OF THE LOAD SHARING OF KNEE LIGAMENTS

2019 ◽  
Author(s):  
Juliana Emery Silva ◽  
Brenno Tavares Duarte ◽  
Rodrigo Ribeiro Pinho Rodarte ◽  
Paulo Pedro Kenedi
Keyword(s):  
Load Sharing ◽  
Knee Ligaments
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