Multivariate Lomax distribution: properties and usefulness in reliability theory

1987 ◽  
Vol 24 (01) ◽  
pp. 170-177 ◽  
Author(s):  
Tapan Kumar Nayak
Keyword(s):  
Reliability Theory ◽  
Multivariate Distributions ◽  
Common Environment ◽  
Lomax Distribution ◽  
Multivariate Generalization ◽  
Multivariate Lomax Distribution

A model incorporating the effect of a common environment on several components (structurally independent) of a system is developed. A multivariate generalization of the Lomax (Pareto type 2) distribution is obtained by mixing exponential variables. Its relationship to other multivariate distributions is discussed. Several properties of this distribution are reported and their usefulness in reliability theory indicated. Finally, a further generalization of this multivariate Lomax distribution is presented.

Multivariate Lomax distribution: properties and usefulness in reliability theory

1987 ◽  
Vol 24 (1) ◽  
pp. 170-177 ◽  
Author(s):  
Tapan Kumar Nayak
Keyword(s):  
Reliability Theory ◽  
Multivariate Distributions ◽  
Common Environment ◽  
Lomax Distribution ◽  
Multivariate Generalization ◽  
Multivariate Lomax Distribution

A model incorporating the effect of a common environment on several components (structurally independent) of a system is developed. A multivariate generalization of the Lomax (Pareto type 2) distribution is obtained by mixing exponential variables. Its relationship to other multivariate distributions is discussed. Several properties of this distribution are reported and their usefulness in reliability theory indicated. Finally, a further generalization of this multivariate Lomax distribution is presented.

Multivariate distributions for the life lengths of components of a system sharing a common environment

1986 ◽  
Vol 23 (02) ◽  
pp. 418-431 ◽  
Author(s):  
Dennis V. Lindley ◽  
Nozer D. Singpurwalla
Keyword(s):  
Simple Model ◽  
Parallel System ◽  
Harsh Environment ◽  
Multicomponent Systems ◽  
Early Failure ◽  
Multivariate Distributions ◽  
Common Environment ◽  
The Common

In assessing the reliability of a system of components, it is usual to suppose the components to fail independently of each other. Often this is inappropriate because the common environment acting on all components induces correlation. For example, a harsh environment will encourage early failure of all components. A simple model that incorporates such dependencies is described, and several properties of this model investigated. Calculations are carried out for a parallel system of two components. Inequalities for multicomponent systems are suggested. The results generalize easily.

Some Characterizations of a Multivariate Lomax Distribution Within the Class of Generalised Mixtures of Exponential Distributions

1997 ◽  
Vol 47 (1-2) ◽  
pp. 11-21 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Closure Properties ◽  
Lomax Distribution ◽  
Selection Of ◽  
Multivariate Lomax Distribution

Selection of the Lomax model through characterization results from amongst the class of continuous mixtures of exponential distributions has been examined. Properties covered are in main based on crude measures of hazard rate and mean residual life. Some closure properties have also been used for this purpose.

On the Reliability Function of A K-Out-Of-N System of Components Sharing a Common Environment

1997 ◽  
Vol 47 (3-4) ◽  
pp. 223-232 ◽  
Author(s):  
Gopal Chaudhuri
Keyword(s):  
Random Environment ◽  
General Condition ◽  
Reliability Function ◽  
Reliability Theory ◽  
Common Environment ◽  
Life Distributions ◽  
Component Failures

The reliability function of a k-out-of- n system which operates in a random environment is studied and compared with the reliability function obtained under the assumption of independence of component-failures. A crossing property of the reliability functions is established under a fairly general condition. It is shown that the reliability function of the system does not belong to any of the aging classes of life distributions considered in the reliability theory.

Multivariate distributions for the life lengths of components of a system sharing a common environment

1986 ◽  
Vol 23 (2) ◽  
pp. 418-431 ◽  
Author(s):  
Dennis V. Lindley ◽  
Nozer D. Singpurwalla
Keyword(s):  
Simple Model ◽  
Parallel System ◽  
Harsh Environment ◽  
Multicomponent Systems ◽  
Early Failure ◽  
Multivariate Distributions ◽  
Common Environment ◽  
The Common

In assessing the reliability of a system of components, it is usual to suppose the components to fail independently of each other. Often this is inappropriate because the common environment acting on all components induces correlation. For example, a harsh environment will encourage early failure of all components. A simple model that incorporates such dependencies is described, and several properties of this model investigated. Calculations are carried out for a parallel system of two components. Inequalities for multicomponent systems are suggested. The results generalize easily.

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