Extensions of the Freund Distribution with Applications in Reliability Theory

Shaked, Moshe

doi:10.1287/opre.32.4.917

Cited by 14 publications

(3 citation statements)

References 13 publications

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“…It can be shown in this case (see [6]) that the time of system failure has the stronger than NBU property of being an increasing failure rate on average (IFRA) distribution. We do not know if this result can be extended to the case n > 2.…”

Section: P{t > S + T I T > S} T)mentioning

confidence: 92%

A model in which component failure rates depend on the working set

Ross

1984

Naval Research Logistics

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We consider a multicomponent system in which the failure rate of a given component at any time depends on the set of working components at that time. Sufficient conditions are presented under which such a system has a life distribution of specified type. The Laplace transform of the time until all components are down is derived. When repair is allowed, conditions under which the resulting process is time reversible are presented.

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Section: P{t > S + T I T > S} T)mentioning

confidence: 92%

A model in which component failure rates depend on the working set

Ross

1984

Naval Research Logistics

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“…An extension to a model with Weibull component lifetime distributions was discussed in Lu, Spurrier and Weier, and Shaked . In Asha et al, a generalization of was proposed as follows.…”

Section: Introductionmentioning

confidence: 99%

Reliability modelling incorporating load share and frailty

Asha

Raja

Равишанкер

2017

Appl Stoch Models Bus & Ind

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The stochastic behaviour of lifetimes of a two component system is often primarily influenced by the system structure and by the covariates shared by the components. Any meaningful attempt to model the lifetimes must take into consideration the factors affecting their stochastic behaviour. In particular, for a load share system, we describe a reliability model incorporating both the load share dependence and the effect of observed and unobserved covariates. The model includes a bivariate Weibull to characterize load share, a positive stable distribution to describe frailty, and also incorporates effects of observed covariates.We investigate various interesting reliability properties of this model using cross ratio functions and conditional survivor functions. We implement maximum likelihood estimation of the model parameters and discuss model adequacy and selection. We illustrate our approach using a simulation study. For a real data situation, we demonstrate the superiority of the proposed model that incorporates both load share and frailty effects over competing models that incorporate just one of these effects. An attractive and computationally simple cross-validation technique is introduced to reconfirm the claim. We conclude with a summary and discussion. KEYWORDSbivariate Weibull distribution, load sharing dependence, maximum likelihood estimation, positive stable frailty, proportional hazards model 206

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“…In the literature, various specific parametric models for bivariate distributions have been suggested and studied. See, for instance, Gumbel (1960), Freund (1961), Marshall and Olkin (1967), Downton (1970), Hawkes (1972), Block and Basu (1974), Shaked (1984), Sarkar (1987) and Hayakawa (1994). A nice review on the modelling of multivariate survival models can be found in Hougaard (1987).…”

Section: Introductionmentioning

confidence: 99%

Construction of two new general classes of bivariate distributions based on stochastic orders

Lee

Hwan

2015

Journal of Multivariate Analysis

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In this paper, based on the concepts of stochastic orders, we propose two new general classes of bivariate distributions. The usual stochastic order and likelihood ratio order are applied to construct the classes. The joint distributions in each class are derived. It will be seen that the obtained formulas for the joint distributions are very simple and easy to apply. Then, the relationships between the classes are discussed and characterized. We illustrate the practical usefulness of the proposed classes by showing that a number of new families of bivariate distributions can be generated from the classes. Furthermore, to illustrate practical relevance, we apply several developed models to analyze a real bivariate failure time data set.

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Extensions of the Freund Distribution with Applications in Reliability Theory

Cited by 14 publications

References 13 publications

A model in which component failure rates depend on the working set

A model in which component failure rates depend on the working set

Reliability modelling incorporating load share and frailty

Construction of two new general classes of bivariate distributions based on stochastic orders

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