Date of Award

6-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD

Abstract

For a parallel system, when one component fails, the failure distribution of the remaining components will have an increased failure rate. This dissertation takes a novel approach to finding the associated failure distribution of the full system using ordinal statistic distributions for correlated Weibull components, allowing for unknown correlations between the dependent components. A Taylor series approximation is presented for the two component; system failure time distributions are also derived for two failures in a two component system, two failures in an n component system, three failures in a three component system, and k failures in an n component system. Additionally, a case study is presented on aircraft turnbuckles. Simulated data is used to illustrate how the derived formulas can be used to create a maintenance plan for the second turnbuckle in the two component system.

AFIT Designator

AFIT-ENC-DS-23-J-001

Comments

A 12-month embargo was observed.

Approved for public release. PA clearance case number on file.

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