Stochastic comparisons and ageing properties of residual lifetime mixture models

Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

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Stochastic comparison of residual lifetime mixture models

Operations Research Letters ◽

10.1016/j.orl.2017.11.015 ◽

2018 ◽

Vol 46 (1) ◽

pp. 122-127 ◽

Cited By ~ 1

Author(s):

Neeraj Misra ◽

Sameen Naqvi

Keyword(s):

Mixture Models ◽

Residual Lifetime ◽

Stochastic Comparison

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Stochastic comparisons of finite mixture models with generalized Lehmann distributed components

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1880592 ◽

2021 ◽

pp. 1-19

Author(s):

Mostafa Sattari ◽

Ghobad Barmalzan ◽

Narayanaswamy Balakrishnan

Keyword(s):

Mixture Models ◽

Finite Mixture Models ◽

Finite Mixture ◽

Stochastic Comparisons ◽

Distributed Components

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Stochastic properties of generalized finite α-mixtures

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964821000243 ◽

2021 ◽

pp. 1-25

Author(s):

Omid Shojaee ◽

Majid Asadi ◽

Maxim Finkelstein

Keyword(s):

Statistical Analysis ◽

Mixture Models ◽

Mixture Model ◽

Real Life ◽

Stochastic Comparisons ◽

Lifetime Distributions ◽

The Real ◽

Stochastic Properties

Most of the real-life populations are heterogeneous and homogeneity is often just a simplifying assumption for the relevant statistical analysis. Mixtures of lifetime distributions that correspond to homogeneous subpopulations were intensively studied in the literature. Various distributional and stochastic properties of finite and continuous mixtures were discussed. In this paper, following recent publications, we develop further a mixture concept in the form of the generalized α-mixtures that include all mixture models that are widely explored in the literature. We study some main stochastic properties of the suggested mixture model, that is, aging and appropriate stochastic comparisons. Some relevant examples and counterexamples are given to illustrate our findings.

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Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Journal of Applied Probability ◽

10.1017/s0021900200013255 ◽

2013 ◽

Vol 50 (01) ◽

pp. 272-287 ◽

Cited By ~ 12

Author(s):

M. Burkschat ◽

J. Navarro

Keyword(s):

Order Statistics ◽

Failure Time ◽

Residual Lifetime ◽

Coherent Systems ◽

Sequential Order ◽

Stochastic Comparisons ◽

Additional Information ◽

Structured Systems ◽

Sequential Order Statistics ◽

Inactivity Time

Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

Download Full-text