Richard K. Burdick

A Review of Methods for Measurement Systems Capability Analysis

We review methods for conducting and analyzing measurement systems capability studies, focusing on the analysis of variance approach. These studies are designed experiments involving crossed and possibly nested factors. The analysis of variance is an attractive method for analyzing the results of these experiments because it permits efficient point and interval estimation of the variance components associated with the sources of variability in the experiment. In this paper we demonstrate computations for the standard two-factor design, describe aspects of designing the experiment, and provide references for situations where the standard two-factor design is not applicable.

Design and analysis of gauge R&R studies : making decisions with confidence intervals in random and mixed ANOVA models

Preface 1. Introduction 2. Balanced One-Factor Random Models 3. Balanced Two-Factor Crossed Random Models with Interaction 4. Design of Gauge R&R Experiments 5. Balanced Two-Factor Crossed Random Models with No Interaction 6. Balanced Two-Factor Crossed Mixed Models 7. Unbalanced One- and Two-Factor Models 8. Strategies for Constructing Intervals with ANOVA Models Appendix A. The Analysis of Variance Appendix B. MLS and GCI Methods Appendix C. Tables of F-values Bibliography Index.

Confidence intervals on linear combinations of variance components that are unrestricted in sign

A new method is proposed for constructing confidence intervals on where the sign of γ is unrestricted and unknown, and are independently distributed chi-squared random variables with ni degrees of freedom for Computer simulation is used to illustrate that the method provides a confidence coefficient that is generally close to the stated level. The method is illustrated by using it to test a main effect in a random three-factor crossed design.

CONFIDENCE INTERVALS ON MEASURES OF VARIABILITY IN R&R STUDIES

Several methods have been proposed for constructing confidence intervals on measures of variability in a classical repeatability and reproducibility study. These methods are compared using computer simulation to determine if the intervals maintain the s..

The Relative Importance of Various Promotional Elements in Different Industrial Purchase Situations

Abstract The relative importance of various promotional elements such as personal selling, trade shows, sales promotions, direct mail, technical literature and trade advertising is examined across five different product types and three different buyclasses. A study of industrial purchasing agents indicated that the relative importance of the promotional elements varied across products but not across buyclasses. Results are discussed and recommendations are made for viewing the importance of promotional elements.

Analysis of a Two-Factor R&R Study With Fixed Operators

The first step of many process improvement projects is to conduct a repeatability and reproducibility (R&R) study. The major objective of such a study is to determine whether a measurement procedure is adequate for monitoring a process. If the measureme..

Using Confidence Intervals to Compare Process Capability Indices

Process capability indices are widely used to measure process performance. In situations such as selecting a supplier and assessing process improvement, it is of interest to compare capability indices for two different processes or the same process before and after an adjustment. In this paper, we consider several methods for performing this comparison on the indices Cpk and Cpm . The methods are compared using a computer simulation. Recommendations are provided for selecting an appropriate method based on power and test size computations.

Confidence Intervals for Misclassification Rates in a Gauge R&R Study

The objective of this paper is to develop a method for constructing confidence intervals for misclassification rates in a gauge repeatability and reproducibility (R&R) study. Confidence intervals are computed using generalized inference methods. Simulation results suggest confidence coefficients are generally greater than the stated value when a sufficient number of parts and operators are selected for the R&R study.

Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures

Abstract In this article we consider the problem of constructing confidence intervals for a linear regression model with unbalanced nested error structure. A popular approach is the likelihood-based method employed by PROC MIXED of SAS. In this article, we examine the ability of MIXED to produce confidence intervals that maintain the stated confidence coefficient. Our results suggest that intervals for the regression coefficients work well, but intervals for the variance component associated with the primary level cannot be recommended. Accordingly, we propose alternative methods for constructing confidence intervals on the primary level variance component. Computer simulation is used to compare the proposed methods. A numerical example and SAS code are provided to demonstrate the methods.

Confidence intervals on ratios of linear combinations for non-disjoint sets of expected mean squares

Abstract A method for constructing confidence intervals on the ratio of expected mean squares p ∑ i=1 P c i θ i − ∑ j=P+1 Q d j θ j ∑ k=1 Q e k θ k , c i , d j , e k ⩾ 0 is proposed. This form of ϱ is different from other ratios for which confidence intervals have been developed because it contains the same expected mean squares in the numerator and denominator. Additionally, it allows negative coefficients in the numerator. Computer simulation is used to examine the confidence coefficients associated with the proposed intervals.