Industrial Statistics with Minitab

Pere Grima, Professor, Department of the Technical University of Catalonia UPC, Barcelona, Spain. Lluis Marco, Assistant Professor, Department of the Technical University of Catalonia UPC, Barcelona, Spain. Xavier Tort-Martorell, Department Director Statistics Department,the Technical University of Catalonia UPC, Barcelona, Spain. Xavier Tort-Martorell is president elect of ENBIS The authors possess a wide experience both in training and consulting. They have designed and delivered courses in various universities and at all levels, from undergraduate to postgraduate and professional training. Their activities have always been strongly linked to the business and industrial world. Most recently with a high focus on Six Sigma training and consulting they have certified more than 450 Black Belts in Spain and Latin America- . They have also advised many companies from different sectors on the implementation of quality improvement programs and the proper use of statistical methods. Among others: Hewlett-Packard, Samsung electronics, Alstom Transport, Siemens VDO, BBVA, Procter & Gamble and ITP.

Preface xiii

Part One Introduction and Graphical Techniques 1

1 A First Look 3

1.1 Initial Screen 3

1.2 Entering Data 4

1.3 Saving Data: Worksheets and Projects 5

1.4 Data Operations: An Introduction 5

1.5 Deleting and Inserting Columns and Rows 7

1.6 First Statistical Analyses 8

1.7 Getting Help 10

1.8 Personal Configuration 12

1.9 Assistant 13

1.10 Any Difficulties? 14

2 Graphics for Univariate Data 15

2.1 File ‘PULSE’ 15

2.2 Histograms 16

2.3 Changing the Appearance of Histograms 17

2.4 Histograms for Various Data Sets 21

2.5 Dotplots 23

2.6 Boxplots 24

2.7 Bar Diagrams 25

2.8 Pie Charts 27

2.9 Updating Graphs Automatically 28

2.10 Adding Text or Figures to a Graph 29

3 Pareto Charts and Cause–Effect Diagrams 31

3.1 File ‘DETERGENT’ 31

3.2 Pareto Charts 32

3.4 Cause-and-Effect Diagrams 35

4 Scatterplots 37

4.1 File ‘pulse’ 37

4.2 Stratification 38

4.3 Identifying Points on a Graph 39

4.4 Using the ‘Crosshairs’ Option 45

4.5 Scatterplots with Panels 46

4.6 Scatterplots with Marginal Graphs 48

4.7 Creating an Array of Scatterplots 50

5 Three Dimensional Plots 52

5.1 3D Scatterplots 52

5.2 3D Surface Plots 55

5.3 Contour Plots 58

6 Part One: Case Studies – Introduction and Graphical Techniques 62

6.1 Cork 62

6.2 Copper 68

6.3 Bread 73

6.4 Humidity 76

Part Two Hypothesis Testing. Comparison of Treatments 79

7 Random Numbers and Numbers Following a Pattern 81

7.1 Introducing Values Following a Pattern 81

7.2 Sampling Random Data from a Column 83

7.3 Random Number Generation 83

7.4 Example: Solving a Problem Using Random Numbers 85

8 Computing Probabilities 87

8.1 Probability Distributions 87

8.2 Option ‘Probability Density’ or ‘Probability’ 88

8.3 Option ‘Cumulative Probability’ 89

8.4 Option ‘Inverse Cumulative Probability’ 89

8.5 Viewing the Shape of the Distributions 92

8.6 Equivalence between Sigmas of the Process and Defects per Million Parts Using ‘Cumulative Probability’ 92

9 Hypothesis Testing for Means and Proportions. Normality Test 95

9.1 Hypothesis Testing for One Mean 95

9.2 Hypothesis Testing and Confidence Interval for a Proportion 99

9.3 Normality Test 100

10 Comparison of Two Means, Two Variances or Two Proportions 103

10.1 Comparison of Two Means 103

10.2 Comparison of Two Variances 107

10.3 Comparison of Two Proportions 109

11 Comparison of More than Two Means: Analysis of Variance 110

11.1 ANOVA (Analysis of Variance) 110

11.2 ANOVA with a Single Factor 110

11.3 ANOVA with Two Factors 114

11.4 Test for Homogeneity of Variances 119

12 Part Two: Case Studies – Hypothesis Testing. Comparison of Treatments 120

12.1 Welding 120

12.2 Rivets 124

12.3 Almonds 126

12.4 Arrow 127

12.5 U Piece 131

12.6 Pores 133

Part Three Measurement Systems Studies and Capability Studies 137

13 Measurement System Study 139

13.1 Crossed Designs and Nested Designs 139

13.2 File ‘RR_CROSSED’ 140

13.3 Graphical Analysis 140

13.4 R&R Study for the Data in File ‘RR_CROSSED’ 141

13.5 File ‘RR_NESTED’ 147

13.6 Gage R&R Study for the Data in File ‘RR_NESTED’ 147

13.7 File ‘GAGELIN’ 148

13.8 Calibration and Linearity Study of the Measurement System 148

14 Capability Studies 151

14.1 Capability Analysis: Available Options 151

14.2 File ‘VITA_C’ 152

14.3 Capability Analysis (Normal Distribution) 152

14.4 Interpreting the Obtained Information 152

14.5 Customizing the Study 154

14.6 ‘Within’ Variability and ‘Overall’ Variability 155

14.7 Capability Study when the Sample Size is Equal to One 158

14.8 A More Detailed Data Analysis (Capability Sixpack) 161

15 Capability Studies for Attributes 163

15.1 File ‘BANK’ 163

15.2 Capability Study for Variables that Follow a Binomial Distribution 163

15.3 File ‘OVEN_PAINTED’ 166

15.4 Capability Study for Variables that Follow a Poisson Distribution 166

16 Part Three: Case Studies – R&R Studies and Capability Studies 168

16.1 Diameter_measure 168

16.2 Diameter_capability_1 173

16.3 Diameter_capability_2 174

16.4 Web_visits 176

Part Four Multi-Vari Charts and Statistical Process Control 181

17 Multi-Vari Charts 183

17.1 File ‘MUFFIN’ 183

17.2 Multi-Vari Chart with Three Sources of Variation 184

17.3 Multi-Vari Chart with Four Sources of Variation 186

18 Control Charts I: Individual Observations 188

18.1 File ‘CHLORINE’ 188

18.2 Graph of Individual Observations 188

18.3 Customizing the Graph 191

18.4 I Chart Options 192

18.5 Graphs of Moving Ranges 196

18.6 Graph of Individual Observations – Moving Ranges 197

19 Control Charts II: Means and Ranges 198

19.1 File ‘VITA_C’ 198

19.2 Means Chart 199

19.3 Graphs of Ranges and Standard Deviations 200

19.4 Graphs of Means-Ranges 201

19.5 Some Ideas on How to Use Minitab as a Simulator of Processes for Didactic Reasons 201

20 Control Charts for Attributes 204

20.1 File ‘MOTORS’ 204

20.2 Plotting the Proportion of Defective Units (P) 204

20.3 File ‘CATHETER’ 205

20.4 Plotting the Number of Defective Units (NP) 206

20.5 Plotting the Number of Defects per Constant Unit of Measurement (C) 208

20.6 File ‘FABRIC’ 210

20.7 Plotting the Number of Defects per Variable Unit of Measurement (U) 210

21 Part Four: Case Studies – Multi-Vari Charts and Statistical Process Control 212

21.1 Bottles 212

21.2 Mattresses (1st Part) 217

21.3 Mattresses (2nd Part) 221

21.4 Plastic (1st Part) 223

21.5 Plastic (2nd Part) 224

Part Five Regression and Multivariate Analysis 231

22 Correlation and Simple Regression 235

22.1 Correlation Coefficient 235

22.2 Simple Regression 238

22.3 Simple Regression with ‘Fitted Line Plot’ 239

22.4 Simple Regression with ‘Regression’ 244

23 Multiple Regression 247

23.1 File ‘CARS2’ 247

23.2 Exploratory Analysis 247

23.3 Multiple Regression 249

23.4 Option Buttons 250

23.5 Selection of the Best Equation: Best Subsets 252

23.6 Selection of the Best Equation: Stepwise 254

24 Multivariate Analysis 256

24.1 File ‘LATIN_AMERICA’ 256

24.2 Principal Components 257

24.3 Cluster Analysis for Observations 263

24.4 Cluster Analysis for Variables 266

24.5 Discriminant Analysis 267

25 Part Five: Case Studies – Regression and Multivariate Analysis 272

25.1 Tree 272

25.2 Power Plant 278

25.3 Wear 285

25.4 TV Failure 290

Part Six Experimental Design and Reliability 293

26 Factorial Designs: Creation 295

26.1 Creation of the Design Matrix 295

26.2 Design Matrix with Data Already in the Worksheet 301

27 Factorial Designs: Analysis 303

27.1 Calculating the Effects and Determining the Significant Ones 303

27.2 Interpretation of Results 308

27.3 A Recap with a Fractional Factorial Design 310

28 Response Surface Methodology 313

28.1 Matrix Design Creation and Data Collection 313

28.2 Analysis of the Results 317

28.3 Contour Plots and Response Surface Plots 322

29 Reliability 325

29.1 File 325

29.2 Nonparametric Analysis 326

29.3 Identification of the Best Model for the Data 329

29.4 Parametric Analysis 330

29.5 General Graphical Display of Reliability Data 333

30 Part Six: Case Studies – Design of Experiments and Reliability 335

30.1 Cardigan 335

30.2 Steering wheel – 1 340

30.3 Steering Wheel – 2 343

30.4 Paper Helicopters 345

30.5 Microorganisms 349

30.6 Jam 359

30.7 Photocopies 365

Appendices 371

A1 Appendix 1: Answers to Questions that Arise at the Beginning 373

A2 Appendix 2: Managing Data 377

A2.1 Copy Columns with Restrictions (File: ‘PULSE’) 377

A2.2 Selection of Data when Plotting a Graph 381

A2.3 Stacking and Unstacking of Columns (File ‘BREAD’) 382

A2.4 Coding and Sorting Data 386

A3 Appendix 3: Customization of Minitab 390

A3.1 Configuration Options 390

A3.2 Use of Toolbars 392

A3.3 Add Elements to an Existing Toolbar 392

A3.4 Create Custom Toolbars 393

Index 397