Campus Units

Industrial and Manufacturing Systems Engineering, Statistics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

2016

Journal or Book Title

Quality Engineering

Volume

28

Issue

1

First Page

3

Last Page

16

DOI

10.1080/08982112.2015.1100440

Abstract

In broad terms, effective probability modeling of modern measurement requires the development of (usually parametric) distributions for increasingly complex multivariate outcomes driven by the physical realities of particular measurement technologies. “Differences” between measures of distribution center and truth function as “bias.” Model features that allow hierarchical compounding of variation function to describe “variance components” like “repeatability,” “reproducibility,” “batch-to-batch variation,” etc. Mixture features in models allow for description (and subsequent downweighting) of outliers. For a variety of reasons (including high-dimensionality of parameter spaces relative to typical sample sizes, the ability to directly include “Type B” considerations in assessing uncertainty, and the relatively direct path to uncertainty quantification for the real objectives of measurement), Bayesian methods of inference in these models are increasingly natural and arguably almost essential.

We illustrate the above points first in an overly simple but instructive example. We then provide a set of formalisms for expressing these notions. Then we illustrate them with real modern measurement applications including (1) determination of cubic crystal orientation via electron backscatter diffraction, (2) determination of particle size distribution through sieving, and (3) analysis of theoretically monotone functional responses from thermogravimetric analysis in a materials study.

Comments

This is an Accepted Manuscript of an article published by Taylor & Francis in Quality Engineering on January 29, 2016, available online: http://www.tandfonline.com/10.1080/08982112.2015.1100440.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

Copyright Owner

Taylor & Francis

Language

en

File Format

application/pdf

Published Version

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