Table of Contents
About the Author
Acknowledgments
Introduction
PART ONE: THE FOUNDATIONS OF DATA ANALYSIS
Chapter One - Four Statistical Problems
1.1 Descriptive Statistics
1.2 Probability Theory
1.3 Statistical Inference
1.4 The Homogeneity Question
1.5 Two Perspectives on These Problems
1.6 Axioms of Data Analysis
1.7 Summary
Chapter Two - Descriptive Statistics and Homogeneity
2.1 What Does the Standard Deviation Statistic Do?
2.2 What Descriptive Statistics Do Not Do
2.3 Local Measures of Dispersion
2.4 Are the Data Homogeneous?
2.5 The Difference Between Global and Local
Chapter Three - Process Behavior Charts
3.1 The Chart for Individual Values
3.2 What Do We Gain from the mR Chart?
3.3 What Makes the XmR Chart Work?
3.4 How Many Values Do I Need?
3.5 Rules for Detecting Nonhomogeneity
3.6 Average and Range Charts
3.7 Chunky Data
3.8 Caution Regarding Software
3.9 Where Do We Go from Here?
Chapter Four - Statistics, Parameters, and Inference
4.1 The Concept of a Probability Model
4.2 Some Cautions Regarding Probability Models
4.3 Elements of a Statistical Inference
4.4 Interval Estimates of Location
4.5 Interval Estimates of Dispersion
4.6 Practical Statistical Inference
4.7 Interpreting "Degrees of Freedom"
4.8 Summary
PART TWO: THE TECHNIQUES OF DATA ANALYSIS
Chapter Five - Data Collected Under One Condition
5.1 What Can We Say About Our Process?
5.2 But What About the Significance Levels?
5.3 Bead Board No. 3
5.4 The Data for NB10
5.5 Summary
Chapter Six - Data Collected Under Two Conditions
6.1 Detecting a Difference with Histograms
6.2 Detecting a Difference with XmR Charts
6.3 Using an Average and Range Chart
6.4 The Analysis of Means
6.5 The Two Sample Student's t-test
6.6 The Paired t-test
6.7 NB10 Revisited
6.8 Summary of Comparing Two Conditions
Chapter Seven - Data Collected Under Three or More Conditions
7.1 XmR Charts for Each Treatment
7.2 Average and Range Charts
7.3 Analysis of Means (ANOM)
7.4 Analysis of Variance (ANOVA)
7.5 The Tukey Post-Hoc Test
7.6 NB10 Again
7.7 Summary of Comparing Several Conditions
Chapter Eight - Data Collected at Three or More Values for X
8.1 The Universe Had a Definite Beginning
8.2 Evaluating Terms in a Model
8.3 Regression: One Line or Two?
8.4 A Deterministic Relation with Controlled X
8.5 A Deterministic Relation with Uncertain X Values
8.6 X and Y are Random Variables
8.7 Data Snooping
8.8 Trends
8.9 The Role of the Scatterplot
8.10 The Problem of Regression Models
Chapter Nine - Count-Based Data
9.1 Two Types of Counts
9.2 Interval Estimates for Universe Proportions
9.3 Homogeneity for Counts
9.4 Should I Compare Counts or Rates?
9.5 A Caution Regarding Counts on an XmR Chart
9.6 Outliers or Signals?
9.7 Comparing Two Proportions with Charts
9.8 Comparing Two Single Proportions
9.9 Comparing Proportions for Several Conditions
9.10 Summary
Chapter Ten - Counts of Events
10.1 Inference for Counts of Events: One Condition
10.2 Using the Poisson Model
10.3 Comparing Two Conditions
10.4 Comparing Several Conditions
10.5 Summary
Chapter Eleven - Counts for Three or More Categories
11.1 Categorical Frequencies for One Condition
11.2 Categorical Data for Two or More Conditions
11.3 Summary
PART THREE: THE KEYS TO EFFECTIVE DATA ANALYSIS
Chapter Twelve - The Dual Nature of Trouble
12.1 "We Are In Trouble"
12.2 A New Definition of Trouble
12.3 The Four Possibilities for Any Process
12.4 Research and Experimentation Are Not Enough
12.5 Operating a Process Predictably
12.6 Summary
Chapter Thirteen - Capability and Performance Indexes
13.1 The Voices(s) of the Process
13.2 The Voice of the Customer
13.3 The Capability Ratio Cp
13.4 The Centered Capability Ratio Cpk
13.5 The Performance Ratio Pp
13.6 The Centered Performance Ratio Ppk
13.7 The Ratios and the Four Possibilities
13.8 Operational Improvement
13.9 Short-Term and Long-Term Capability
13.10 Interpreting and Using Capability Indexes
13.11 Summary
Chapter Fourteen - Using the Effective Cost of Production
14.1 The Effective Cost of Production
14.2 The Benchmark Cost of Production
14.3 The Centered Cost of Production
14.4 The Predictable Cost of Production
14.5 The Minimum Cost of Production
14.6 Using the Effective Cost of Production
14.7 Summary
Chapter Fifteen - The Basis for the Effective Cost of Production
15.1 The Structure of the Effective Cost of Production
15.2 The Average Excess Costs
15.3 Finding the Effective Cost of Production
15.4 Summary of ECP for Measurements
15.5 Effective Costs of Production for Counts of Items
15.6 Effective Costs of Production for Counts of Events
Chapter Sixteen - The Six Sigma Zone
16.1 The Effective Cost of Production Curves
16.2 An Illustration
16.3 The Six Sigma Zone
16.4 Summary
Chapter Seventeen - Some Problems
17.1 Problems with Defects Per Million
17.2 Problems with Defects Per Million Opportunities
17.3 Problems with FMEA Risk Priority Numbers
17.4 Problems with Special Causes
17.5 Problems with DMAIC Models
17.6 Do We Need a Gauge R&R Study?
17.7 Problems with Narrowly Defined Projects
17.8 Summary
Chapter Eighteen - Two Models for Process Improvement
18.1 Getting Started
18.2 Characterize the Status of the Process Outcomes
18.3 Outcomes in the State or Brink of Chaos
18.4 Outcomes in the Threshold State
18.5 Outcomes in the Ideal State
18.6 Focusing Improvements on Strategic Objectives
18.7 Summary
Appendix
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 Average and Std.Dev. Charts Based on the Average s
Table A.6 Average and Std.Dev. Charts Based on the Median s
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
Table A.10 Overall Alpha-Levels for Range Charts
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 Cp and Pp
Table A.16 Factors for 90% Interval Estimates of Cpk and Ppk
Table A.17 The Effective Cost of Production - when all nonconforming units are scrapped
Table A.18 The Effective Cost of Production - when all nonconforming units are reworked
Table A.19 The Effective Cost of Production - when the cost of rework is 0.50 of the cost of scrap and the Average is on the SCRAP side of the target
Table A.20 The Effective Cost of Production - when the cost of rework is 0.50 of the cost of scrap and the Average is on the REWORK side of the target
Table A.21 Effective Costs of Production based on Counts of Items - when Rework Salvages NO Raw Material
Table A.22 Effective Costs of Production based on Counts of Items - when Rework Salvages Material Worth 25% of Nominal Cost
Table A.23 Effective Costs of Production based on Counts of Items - when Rework Salvages Material Worth 50% of Nominal Cost
Table A.24 Effective Costs of Production based on Counts of Items - when Rework Salvages Material Worth 75% of Nominal Cost
Index