Industrial Statistics with Minitab

Pere Grima Cintas, Lluis Marco-Almagro and Xavier Tort-Martorell Llabres, Universitat Politecnica de Catalunya. BarcelonaTech Barcelona, Spain

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