Estimation and testing with extended sequential order statistics

Tim Pesch

doi:10.26182/76j2-f113

Estimation and testing with extended sequential order statistics

Tim Pesch

Research output: Thesis › Doctoral Thesis

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Abstract

The lifetimes of heterogeneous components from a load-share system can adequately be represented by the model of Extended Sequential Order Statistics (ESOS). In this thesis, we will present a series of exciting inferential results including different types of maximum likelihood estimators (MLEs) of the underpinning model and distribution parameters and a likelihood ratio test to test whether the assumption of heterogeneous components is justified. The ESOS model is powerful but features a large number of parameters. We introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Polpo, Adriano, Supervisor Cripps, Edward, Supervisor Cramer, Erhard, Supervisor, External person
Thesis sponsors	Australian Government Research Training Program
Award date	11 Dec 2024
DOIs	https://doi.org/10.26182/76j2-f113
Publication status	Unpublished - 2024

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10.26182/76j2-f113

THESIS - DOCTOR OF PHILOSOPHY - PESCH Tim Michael - 2024
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3 Article

Estimation with extended sequential order statistics: A link function approach
Pesch, T., Cramer, E., Polpo, A. & Cripps, E., 1 Sept 2024, In: Applied Stochastic Models in Business and Industry. 40, 5, p. 1313-1336 24 p.
Research output: Contribution to journal › Article › peer-review

Open Access
Modeling Failure Risks in Load-Sharing Systems With Heterogeneous Components
Pesch, T. M., Cramer, E., Cripps, E. & Polpo, A., 2024, In: IEEE Transactions on Reliability. 73, 3, p. 1446-1458 13 p.
Research output: Contribution to journal › Article › peer-review
1 Citation (Scopus)
Reliability inference with extended sequential order statistics
Pesch, T., Polpo, A., Cripps, E. & Cramer, E., 1 Jul 2023, In: Applied Stochastic Models in Business and Industry. 39, 4, p. 520-535 16 p.
Research output: Contribution to journal › Article › peer-review

Open Access
3 Citations (Scopus)

Cite this

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title = "Estimation and testing with extended sequential order statistics",

abstract = "The lifetimes of heterogeneous components from a load-share system can adequately be represented by the model of Extended Sequential Order Statistics (ESOS). In this thesis, we will present a series of exciting inferential results including different types of maximum likelihood estimators (MLEs) of the underpinning model and distribution parameters and a likelihood ratio test to test whether the assumption of heterogeneous components is justified. The ESOS model is powerful but features a large number of parameters. We introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model.",

keywords = "load-share model, successive failures, heterogeneous components, non identical distributions, sequential order statistics, link functions, likelihood inference",

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year = "2024",

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language = "English",

school = "The University of Western Australia",

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AB - The lifetimes of heterogeneous components from a load-share system can adequately be represented by the model of Extended Sequential Order Statistics (ESOS). In this thesis, we will present a series of exciting inferential results including different types of maximum likelihood estimators (MLEs) of the underpinning model and distribution parameters and a likelihood ratio test to test whether the assumption of heterogeneous components is justified. The ESOS model is powerful but features a large number of parameters. We introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model.

KW - load-share model

KW - successive failures

KW - heterogeneous components

KW - non identical distributions

KW - sequential order statistics

KW - link functions

KW - likelihood inference

U2 - 10.26182/76j2-f113

DO - 10.26182/76j2-f113

M3 - Doctoral Thesis

ER -

Estimation and testing with extended sequential order statistics

Abstract

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Research output

Estimation with extended sequential order statistics: A link function approach

Modeling Failure Risks in Load-Sharing Systems With Heterogeneous Components

Reliability inference with extended sequential order statistics

Cite this