The Six Sigma Practitioner’s Guide to Data Analysis

1 The Six Sigma practitioner sGuide to Data AnalysisSecond EditionDonald J. WheelerFellow of the American Statistical AssociationFellow of the American Society for QualitySPC PressKnoxville, TennesseevContentsAbout the AuthorxiAcknowledgmentsxiiPreface to the Second EditionxiiIntroductionxiiiPART ONE: THE FOUNDATIONS OF DATA ANALYSIS1 OneFour Statistical Homogeneity Perspectives on These of Data Studies and Experimental Statistics and Does the Standard Deviation Statistic Do? Descriptive Statistics Do Not Measures of the Data Homogeneous? Difference between Global and Local38 ThreeProcess Behavior Chart for Individual Do We Gain from the mR Chart? Makes the XmR Chart Work? Many Values Do I Need for Limits? for Detecting and Range regarding Do We Go from Here?66viFourStatistics, Parameters, and Concept of a Probability Cautions regarding Probability of Statistical Estimates of Estimates of Statistical Degrees of Freedom TWO: THE TECHNIQUES OF DATA ANALYSIS93 FiveData Collected under One Can We Say about Our Process?

2 What about the Significance Levels? Board No. Data for Collected under Two a Difference with a Difference with XmR an Average and Range Analysis of Two-Sample Student s Paired of Comparing Two Conditions130 SevenData Collected under Three or More Charts for Each and Range of of Tukey Post-Hoc of Comparing Several Conditions148viiEightData Collected at Three or More Values for Universe Had a Definite Terms in the : One Line or Two? Deterministic Relation with Controlled X Deterministic Relation with Uncertain X and Y Are Random Role of the Problem of Regression Models171 NineCount-Based Types of Estimates for Universe for I Compare Counts or Rates? Caution regarding Counts on an XmR or Signals? Two Proportions with Two Single Proportions for Several of for Counts of Events: One the Poisson Two Several for Three or More Frequencies for One Data for Two or More THREE.

3 THE KEYS TO EFFECTIVE DATA ANALYSIS219 TwelveThe Dual Nature of We Are in Trouble New Definition of Four Possibilities for Any and Experimentation Are Not a Process and Performance Voice(s) of the Voice of the Capability Ratio, Centered Capability Ratio, Performance Ratio, Centered Performance Ratio, the Four Ratios Ratios and the Four Short-Term and Long-Term Interval Estimates for Capability Summary267 FourteenUsing the Effective Cost of Production and Effective Cost of Production and Baseline Cost of Production and Centered Cost of Production and Predictable Cost of Production and Minimum Cost of Production and the Effective Cost of Production and Basis for the Effective Cost of Production and Structure of the Effective Cost of Production and Average Excess the Effective Cost of Production and of ECP&U for Effective Cost of Production for Counts of Effective Cost of Production for Counts of Events 291ixSixteenThe Six Sigma Effective Cost of Production and Use Six Sigma with Defects per with Defects per Million with FMEA Risk Priority with Special with DMAIC We Need a Gauge R&R Study?

4 With Narrowly Defined 331 EighteenTwo Models for Process the Status of the Process in the State or Brink of in the Threshold in the Ideal Improvement on Strategic Honest Gauge R&R AIAG Gauge R&R Percentages of the Total Percentages of the Specified Number of Distinct Categories AIAG Can You Learn from the AIAG Study? Honest Gauge R&R Correction Factors for Measures of Dispersion368-369 Table Charts: Charts for Individual Values370-371 Table and Range Charts Based on the Average Range372-373 Table and Range Charts Based on the Median Range374-375 Table and Standard Deviation Charts Based on the Average Standard Deviation Statistic376-377 Table and Standard Deviation Charts Based on the Median Standard Deviation Statistic378-379 Table Values for Student s t Distributions380-381 Table of Chi-Square Distributions382-383 Table Alpha-Levels for Average Charts384 Table Overall Alpha-Levels for Range Charts385 Table Quick Scale Factors for Range-Based ANOM386-388 Table Quick Scale Factors for Pooled Variance ANOM389-391 Table Percentiles of the F-Distribution392-397 Table Percentiles of the Studentized Range Distribution.

5 Q398-403 Table Factors for 90% Interval Estimates of Cp and Pp404 Table Factors for 90% Interval Estimates of Cpk and Ppk405 Table The Effective Cost of Production and UseWhen All Nonconforming Units Are Scrapped406-408 Table The Effective Cost of Production and UseWhen All Nonconforming Units Are Reworked409-411 Table The Effective Cost of Production and UseWhen the Cost of Rework Is Half of the Cost of Scrapand the Average Is on the SCRAP Side of the Target412-414 Table The Effective Cost of Production and UseWhen the Cost of Rework Is Half of the Cost of Scrap and the Average Is on the REWORK Side of the Target415-417 Index419