The Six Sigma Practitioner s. Guide to Data Analysis

Transcription

1 The Six Sigma Practitioner s Guide to Data Analysis Second Edition Donald J. Wheeler Fellow of the American Statistical Association Fellow of the American Society for Quality SPC Press Knoxville, Tennessee

2 Contents About the Author xi Acknowledgments xii Preface to the Second Edition xii Introduction xiii PART ONE: THE FOUNDATIONS OF DATA ANALYSIS 1 One Four Statistical Problems Descriptive Statistics Probability Theory Statistical Inference The Homogeneity Question Two Perspectives on These Problems Axioms of Data Analysis Observational Studies and Experimental Studies Summary 17 Two Descriptive Statistics and Homogeneity What Does the Standard Deviation Statistic Do? What Descriptive Statistics Do Not Do Local Measures of Dispersion Are the Data Homogeneous? The Difference between Global and Local 38 Three Process Behavior Charts The Chart for Individual Values What Do We Gain from the mr Chart? What Makes the XmR Chart Work? How Many Values Do I Need for Limits? Rules for Detecting Nonhomogeneity Average and Range Charts Chunky Data Caution regarding Software Where Do We Go from Here? 66 v

3 Four Statistics, Parameters, and Inference The Concept of a Probability Model Some Cautions regarding Probability Models Elements of Statistical Inference Interval Estimates of Location Interval Estimates of Dispersion Practical Statistical Inference Interpreting Degrees of Freedom Summary 91 PART TWO: THE TECHNIQUES OF DATA ANALYSIS 93 Five Data Collected under One Condition What Can We Say about Our Process? But What about the Significance Levels? Bead Board No The Data for NB Summary 107 Six Data Collected under Two Conditions Detecting a Difference with Histograms Detecting a Difference with XmR Charts Using an Average and Range Chart The Analysis of Means The Two-Sample Student s t-test The Paired t-test NB10 Revisited Summary of Comparing Two Conditions 130 Seven Data Collected under Three or More Conditions XmR Charts for Each Treatment Average and Range Charts Analysis of Means Analysis of Variance The Tukey Post-Hoc Test NB10 Again Summary of Comparing Several Conditions 148 vi

4 Eight Data Collected at Three or More Values for X The Universe Had a Definite Beginning Evaluating Terms in the Model Regression: One Line or Two? A Deterministic Relation with Controlled X Values A Deterministic Relation with Uncertain X Values X and Y Are Random Variables Data Snooping Trends The Role of the Scatterplot The Problem of Regression Models 171 Nine Count-Based Data Two Types of Counts Interval Estimates for Universe Proportions Homogeneity for Counts Should I Compare Counts or Rates? A Caution regarding Counts on an XmR Chart Outliers or Signals? Comparing Two Proportions with Charts Comparing Two Single Proportions Comparing Proportions for Several Conditions Summary 196 Ten Counts of Events Inference for Counts of Events: One Condition Using the Poisson Model Comparing Two Conditions Comparing Several Conditions Summary 206 Eleven Counts for Three or More Categories Categorical Frequencies for One Condition Categorical Data for Two or More Conditions Summary 218 vii

5 PART THREE: THE KEYS TO EFFECTIVE DATA ANALYSIS 219 Twelve The Dual Nature of Trouble We Are in Trouble A New Definition of Trouble The Four Possibilities for Any Process Research and Experimentation Are Not Enough Operating a Process Predictably Summary 242 Thirteen Capability and Performance Indexes The Voice(s) of the Process The Voice of the Customer The Capability Ratio, C p The Centered Capability Ratio, C pk The Performance Ratio, P p The Centered Performance Ratio, P pk Using the Four Ratios Together The Ratios and the Four Possibilities Operational Improvement Short-Term and Long-Term Capability Interval Estimates for Capability Indexes Summary 267 Fourteen Using the Effective Cost of Production and Use The Effective Cost of Production and Use The Baseline Cost of Production and Use The Centered Cost of Production and Use The Predictable Cost of Production and Use The Minimum Cost of Production and Use Using the Effective Cost of Production and Use Summary 280 Fifteen The Basis for the Effective Cost of Production and Use The Structure of the Effective Cost of Production and Use The Average Excess Costs Finding the Effective Cost of Production and Use Summary of ECP&U for Measurements The Effective Cost of Production for Counts of Items The Effective Cost of Production for Counts of Events 291 viii

6 Sixteen The Six Sigma Zone The Effective Cost of Production and Use Curves An Illustration The Six Sigma Zone Summary 302 Seventeen Some Problems Problems with Defects per Million Problems with Defects per Million Opportunities Problems with FMEA Risk Priority Numbers Problems with Special Causes Problems with DMAIC Models Do We Need a Gauge R&R Study? Problems with Narrowly Defined Projects Summary 331 Eighteen Two Models for Process Improvement Getting Started Characterize the Status of the Process Outcomes Outcomes in the State or Brink of Chaos Outcomes in the Threshold State Outcomes in the Ideal State Focusing Improvement on Strategic Objectives Summary 341 Nineteen An Honest Gauge R&R Study The AIAG Gauge R&R Study The Percentages of the Total Variation The Percentages of the Specified Tolerance The Number of Distinct Categories The AIAG Guidelines What Can You Learn from the AIAG Study? An Honest Gauge R&R Study Summary 363 ix

7 Appendix 367 Table A.1 Bias Correction Factors for Measures of Dispersion Table A.2 XmR Charts: Charts for Individual Values Table A.3 Average and Range Charts Based on the Average Range Table A.4 Average and Range Charts Based on the Median Range Table A.5 Table A.6 Average and Standard Deviation Charts Based on the Average Standard Deviation Statistic Average and Standard Deviation Charts Based on the Median Standard Deviation Statistic Table A.7 Critical Values for Student s t Distributions Table A.8 Percentiles of Chi-Square Distributions Table A.9 Overall Alpha-Levels for Average Charts 384 Table A.10 Overall Alpha-Levels for Range Charts 385 Table A.11 Quick Scale Factors for Range-Based ANOM Table A.12 Quick Scale Factors for Pooled Variance ANOM Table A.13 Percentiles of the F-Distribution Table A.14 Percentiles of the Studentized Range Distribution, q Table A.15 Factors for 90% Interval Estimates of C p and P p 404 Table A.16 Factors for 90% Interval Estimates of C pk and P pk 405 Table A.17 The Effective Cost of Production and Use When All Nonconforming Units Are Scrapped Table A.18 The Effective Cost of Production and Use When All Nonconforming Units Are Reworked Table A.19 The Effective Cost of Production and Use When the Cost of Rework Is Half of the Cost of Scrap and the Average Is on the SCRAP Side of the Target Table A.20 The Effective Cost of Production and Use When the Cost of Rework Is Half of the Cost of Scrap and the Average Is on the REWORK Side of the Target Index 419 x