Download Quantitative Methods for Interlaboratory Testing

Quantitative Methods for Measuring and Assessing
Uncertainties in Testing Process and Outcomes
(Workshop from July 30 to August 10, 2001
at National Bureau of Standards & Metrology and Inspection, Taiwan)
Carl Lee
Professor of Statistics,
Statistical Consultant and University Assessment Coordinator
Central Michigan University
Mt. Pleasant MI 48859 USA
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Outline of the Workshop
Module One: The Measurements and Uncertainties
•Basic concepts of measuring uncertainty
•Key issues to be considered
•Bias and variability
Module Two: Graphical and numerical exploration of univariate variables
•Planning an inter-laboratory testing
•Graphical tools for demonstrating uncertainty
•Numerical tools for quantifying uncertainty
•Shapes of distributions and relationship to numerical measurements.
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Module Three: Graphical and numerical exploration of bivariate variables
•Scatter Plot and relationship with correlation coefficient
•Least square fitting of linear regression lines
Module Four: Normal distribution and it’s applications to interlaborotary
testing
•The use of standardized normal table
•Empirical Rule – the probability concept of rare event
• Techniques for testing Normality assumption
•Data transformation to approximate normal
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Module Five: Outlier Detection for one sample case
•Box Plot, h-plot and interpretations for one sample case
•Numerical approaches for detecting outliers
•A statistical model for one-sample case
•Use of standardized residuals for outlier detection.
•Use of deleted studentized residuals for outlier detection.
•Statistical quality control charts for monitoring between-lab means and withinlab variations.
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Module Six: Outlier Detection for Two sample case
•Youden Plots and interpretations
•Principal Component Analysis
•Bivariate normal distribution
•Bivariate plots and interpretations
•Marginal plot and its interpretations
•A general statistical model for two-sample cases
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Module Seven: Reporting and presenting uncertainties
•Four conditions in measuring and propagating uncertainty
•No information about the variables
•Variables are independent
•Variables are correlated
•Variables follow a certain probability distribution
•Combining Uncertainty of the same components measured by different individuals
•Standard error of sample mean
•Confidence interval of sample mean
•Uncertainty due to calibration using least square fitting
•Type B uncertainty
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Module Eight:Comparative Study for Inter-laboratory
Testing
• Comparative Study One: Comparing testing results with a given
reference or a given standard
• The concept and Procedure for performing the one sample t-test
•Comparative Study for Inter-laboratory Testing : two-group
cases
•Designing experiments for two-sample comparative study
•Analysis of paired samples
•Analysis of two independent samples
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Module Nine:Techniques for Monitoring Variability and
Testing Homogeneity
•Comparing variance with a standard or reference
•Comparing variances of two groups
•Bonferroni’s simultaneous confidence interval for uncertainty
•Testing uniformity of variances for more than two groups
•Bartlett’s method
•Levene’s method
•Graphical methods for demonstrating and comparing variances
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Module Ten: Planning Experiments – the general
consideration and Comparative Study for more than
two groups
•General consideration of planning experiments
•Local control of errors
•Statistical model for One-way ANOVA
•Residual Analysis for outliers and diagnosis of assumptions
•Data transformation techniques
•Post-Hoc Analysis and Sum of square decomposition
•Contrasts, simultaneous comparison, pair-wise
comparison, comparison with control
•Trend analysis,
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Module Eleven: Experiments to study VariancesVariance Components Analysis and Nested Models
•Variance Component Estimation,
•Intra-correlation
•Mixed Models
•Nested Models with two variance components
•Nested Models with three variance components
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Module Twelve: Designs and Analysis for Factorial
Treatments
•Statistical Model – Two-factor Case
•ANOVA for two-factor Case
•Interactions – concepts, computation and interpretation
•Post-Hoc Comparison
•Techniques of Sum of Squares Decompositions
•Statistical Model – Three Factor Case
•Analysis for Three-factor Case
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Module Thirteen: Gage R&R Analysis – Quantifying
Repeatability and Reproducibility
•
What is Gage R&R Analysis?
•
Statistical model for Gage R&R Crossed Design
•
Estimation of Repeatability and Reproducibility
•
Using X-bar, R-Chart
•
Using ANOVA
•
Statistical Model for Gage R&R Nested Design
•
Use of Generalized Linear Model to analyze Gage R&R Data
•
Gage Capability Index
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Module Fourteen : Block Designs and Others
•Randomized Complete Block Designs
•Statistical Model, Analysis and Interpretation
•Others
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Appendix
1. A Simplified Minitab Manual
2. Data sets
3. References
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