# Confidence intervals for two-dimensional data with circular tolerances in a gauge R&R study

Confidence intervals for two-dimensional data with circular tolerances in a gauge R&R study In this paper, we discuss our application of the Bootstrap method to construct the confidence interval of the diameter for two-dimensional data with circular tolerances in a gauge repeatability and reproducibility study. Factors simulated to validate performance include: the variance component, and sample size. The simulation results show that the Bootstrap method can cover the stated nominal coefficient in most scenarios. There exists a positive correlation between width of confidence intervals and variance components; the width of confidence intervals for diameters is increased when the variance components $${(\hat{{\sigma}}_x^2, \hat{{\sigma}}_y^2\,{\rm or}\,\hat{{\sigma}}_{xy}^2)}$$ are increased. The coverage proportion is not significantly affected by variance-components. Also, the width of confidence interval for the diameter and coverage proportion is not significantly affected by sample size. One real example based on a nested design is used to demonstrate the application of the proposed method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

# Confidence intervals for two-dimensional data with circular tolerances in a gauge R&R study

, Volume 46 (1) – Mar 31, 2010
15 pages

/lp/springer_journal/confidence-intervals-for-two-dimensional-data-with-circular-tolerances-NoWzky85u9
Publisher
Springer Journals
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-010-9326-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we discuss our application of the Bootstrap method to construct the confidence interval of the diameter for two-dimensional data with circular tolerances in a gauge repeatability and reproducibility study. Factors simulated to validate performance include: the variance component, and sample size. The simulation results show that the Bootstrap method can cover the stated nominal coefficient in most scenarios. There exists a positive correlation between width of confidence intervals and variance components; the width of confidence intervals for diameters is increased when the variance components $${(\hat{{\sigma}}_x^2, \hat{{\sigma}}_y^2\,{\rm or}\,\hat{{\sigma}}_{xy}^2)}$$ are increased. The coverage proportion is not significantly affected by variance-components. Also, the width of confidence interval for the diameter and coverage proportion is not significantly affected by sample size. One real example based on a nested design is used to demonstrate the application of the proposed method.

### Journal

Quality & QuantitySpringer Journals

Published: Mar 31, 2010

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