Appendix A: More on Probability and Model Fitting

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Appendix A: More on Probability and Model Fitting

Stephen B. Vardeman & J. Marcus Jobe

This chapter is part of: Vardeman S. & Jobe J. 2023. Basic Engineering Data Collection and Analysis

Description
The introduction to probability theory in Chapter 5 was relatively brief. There are, of course, important engineering applications of probability that require more background in the subject. So this appendix gives a few more details and discusses some additional uses of the theory that are reasonably elementary, particularly in the contexts of reliability analysis and life data analysis. The appendix begins by discussing the formal/axiomatic basis for the mathematics of probability and several of the most useful simple consequences of the basic axioms. It then applies those simple theorems of probability to the prediction of reliability for series, parallel, and combination series-parallel systems. A brief section treats principles of counting (permutations and combinations) that are sometimes useful in engineering applications of probability. There follows a section on special probability concepts used with life-length (or time-to-failure) variables. The appendix concludes with a discussion of maximum likelihood methods for model fitting and drawing inferences.

Description

The introduction to probability theory in Chapter 5 was relatively brief. There are, of course, important engineering applications of probability that require more background in the subject. So this appendix gives a few more details and discusses some additional uses of the theory that are reasonably elementary, particularly in the contexts of reliability analysis and life data analysis. The appendix begins by discussing the formal/axiomatic basis for the mathematics of probability and several of the most useful simple consequences of the basic axioms. It then applies those simple theorems of probability to the prediction of reliability for series, parallel, and combination series-parallel systems. A brief section treats principles of counting (permutations and combinations) that are sometimes useful in engineering applications of probability. There follows a section on special probability concepts used with life-length (or time-to-failure) variables. The appendix concludes with a discussion of maximum likelihood methods for model fitting and drawing inferences.

Details

Published	Published By	Pages
Jan. 12, 2023	Iowa State University Digital Press	57
License Information
© 2001 Stephen B. Vardeman and J. Marcus Jobe. Basic Engineering Data Collection and Analysis is available under a Creative Commons Attribution NonCommercial ShareAlike (CC BY-NC-SA) 4.0 International license. You may share and adapt the material, so long as you provide appropriate credit to the original authors, do not use the material for commercial purposes, and any adaptations or remixes of the material which you create are distributed under the same license as the original.
Citation
Vardeman S. & Jobe J. 2023. Appendix A: More on Probability and Model Fitting. In Vardeman S. & Jobe J. 2023. Basic Engineering Data Collection and Analysis