Computer Science

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Overview of Applications in the Book, by Discipline

Accounting Accounts receivable 285, 297 Auditing for price errors 329 Developing a flexible budget 537 Estimating total tax refunds 325 Estimating total taxable income 325 Overhead cost analysis 423, 437, 471, 490, 520, 524

Economics/Government Demand and cost for electricity 461 Demand for desktops and laptops 402 Demand for French bread 481 Demand for heating oil 536 Demand for microwaves 182 Electricity pricing 736 Home and condo prices 78 Housing price structure 480 Presidential elections 19 Sales of new houses 566, 572

Finance Bond investment strategy 893 Capital budgeting 714 Cash management 852 DJIA index 58, 77 Investing for college 892 Investing for retirement 481, 857 Investment strategy 703 Investor’s after-tax profit 181 Land purchase decision 274 Liquidity risk management 829 Market return scenarios 152, 157 Mutual fund returns 171, 195 New car development 847 Pension fund management 708 Portfolio analysis 743 Random walk of stock prices 562 Stock hedging 757

Human Resources Employee empowerment 389 Employee retention 361 Gender discrimination 450, 457, 514 Jobs in statistics and mathematics 897 Personnel testing 178 Productivity due to exercise 384

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Marketing Catalog marketing 503, 508 Churn in cellular phone market 136 Clustering shoe customers 934 Customer complaints 349, 378 Customer valuation 865 DVD movie renters 310 Electronics sales 108 Frozen lasagna dinner buyers 125, 915, 919, 923 Furniture pricing 480 Marketing and selling condos 873 New pizza style decisions 365, 373 New product decisions 233, 240, 243, 260 Olympics sponsors 363 Response to new sandwich 319, 346, 348 Running shoe style decisions 274 Sales presentation ratings 339 Sales response to coupons 343 Sales versus promotions 421, 433 Soft-drink can style decisions 380 Supermarket sales 197 Supermarket transactions 27 Value of free maintenance agreement 868

Miscellaneous Statistical Crime in the U.S. 54 Cruise ship entertainment 16 Election returns 200 Family income sampling 283 Forecasting U.S. population 557 IQ and bell curve 166 Predictors of successful movies 79, 482 Questionnaire responses 23 Relationship between smoking and drinking 82 Removing Vioxx from market 412 Sample size determination in legal case 279 Saving, spending, social climbing 136 Simpson’s paradox 165 University admissions 360

Operations Management Aggregate planning 693 Airline boarding strategies 759 Airline hub location decisions 729 Arrivals at bank 135 Automobile production 755 Battery lifetimes 191 Bidding for contracts 831 Blending oil 670 Developing Army helicopter component 276

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Developing electronic timing system 275 Delivery times at restaurant 361 Distribution of metal strip widths 396 Employee scheduling 663 Expensive watch production 219 Forecasting sales 551, 554, 559, 566, 572, 576, 581, 586 Inventory management 208 Learning curve for production 466 Manufacturing plastics operations 599 Ordering decisions 781, 784, 796, 806, 812, 815 Out-of-spec products 350 Overbooking at airlines 198 Product mix decisions 603, 631, 721 Production quantity decisions 827, 828 Production scheduling 641, 840 Production, inventory, distribution decisions 661 Quality control at paper company 179 Reliability of motors 336 Site selection of motor inns 417 Timing uncertainty in construction 144 Transportation, logistics decisions 677, 686 Variability in machine parts 333 Warranty costs 835

Sports/Gaming Baseball salaries 31, 40, 46, 49, 88 Games at McDonald’s 139 Golf stats on PGA tour 95 NCAA basketball tournament simulation 882 Revenue management at casino 539 Streak shooting in basketball 201 Wheel of fortune simulation 300 Winning at craps 879 Winning the lottery 220

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Australia • Brazil • Mexico • Singapore • United Kingdom • United States

Business Analytics: Data Analysis and Decision Making

6th Edition

S. Christian Albright Kelly School of Business, Indiana University, Emeritus

Wayne L. Winston Kelly School of Business, Indiana University

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Business Analytics: Data Analysis & Decision Making, Sixth Edition

S. Christian Albright and Wayne L. Winston

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To my wonderful wife Mary—my best friend and travel mate; to Sam, Lindsay, Teddy, and Archie; and to Bryn, our ball-playing Welsh corgi!Archie; and to Bryn, our ball-playing Welsh corgi! S.C.A

To my wonderful familyTo my wonderful family W.L.W.

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S. Christian Albright got his B.S. degree in Mathematics from Stanford in 1968 and his PhD in Operations Research from Stanford in 1972. He taught in the Operations & Decision Technologies Department in the Kelley School of Business at Indiana University (IU) for close to 40 years, before retiring from teaching in 2011. While at IU, he taught courses in management science, computer simulation, statistics, and computer programming to all levels of business students, including undergraduates, MBAs, and doctoral students. In addition,

he taught simulation modeling at General Motors and Whirlpool, and he taught database analysis for the Army. He published over 20 articles in leading operations research journals in the area of applied probability, and he has authored the books Statistics for Business and Economics, Practical Management Science, Spreadsheet Modeling and Applications, Data Analysis for Managers, and VBA for Modelers. He worked for several years after “retirement” with the Palisade Corporation developing training materials for its software products, he has developed a commercial version of his Excel® tutorial, called ExcelNow!, and he continues to revise his textbooks.

On the personal side, Chris has been married for 44 years to his wonderful wife, Mary, who retired several years ago after teaching 7th grade English for 30 years. They have one son, Sam, who lives in Philadelphia with his wife Lindsay and their two sons, Teddy and Archer. Chris has many interests outside the academic area. They include activities with his family (especially traveling with Mary), going to cultural events at IU, power walking while listening to books on his iPod, and reading. And although he earns his livelihood from statistics and management science, his real passion is for playing real passion is for playing real classical piano music.

Wayne L. Winston taught in the Operations & Decision Technologies Department in the Kelley School of Business at Indiana University for close to 40 before retiring a few years ago. Wayne received his B.S. degree in Mathematics from MIT and his PhD in Operations Research from Yale. He has written the successful textbooks Operations Research: Applications and Algorithms, Mathematical Programming: Applications and Algorithms, Simulation Modeling Using @RISK, Practical Management Science, Data Analysis and Decision Making, Financial Models

Using Simulation and Optimization, and Mathletics. Wayne has published more than 20 articles in leading journals and has won many teaching awards, including the school-wide MBA award four times. He has taught classes at Microsoft, GM, Ford, Eli Lilly, Bristol-Myers Squibb, Arthur Andersen, Roche, PricewaterhouseCoopers, and NCR, and in “retirement,” he is currently teaching several courses at the

About the Authors

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University of Houston. His current interest is showing how spreadsheet models can be used to solve business problems in all disciplines, particularly in finance and marketing.

Wayne enjoys swimming and basketball, and his passion for trivia won him an appearance several years ago on the television game show Jeopardy!, where he won two games. He is married to the lovely and talented Vivian. They have two children, Gregory and Jennifer.

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vi

Brief Contents

Preface xviii 1 Introduction to Business Analytics 1

Part 1 Exploring Data 17 2 Describing the Distribution of a Single Variable 19 3 Finding Relationships among Variables 79

Part 2 Probability and Decision Making Under Uncertainty 137

4 Probability and Probability Distributions 139 5 Normal, Binomial, Poisson, and Exponential Distributions 166 6 Decision Making under Uncertainty 222

Part 3 Statistical Inference 277 7 Sampling and Sampling Distributions 279 8 Confidence Interval Estimation 311 9 Hypothesis Testing 363

Part 4 Regression Analysis and Time Series Forecasting 415 10 Regression Analysis: Estimating Relationships 417 11 Regression Analysis: Statistical Inference 482 12 Time Series Analysis and Forecasting 539

Part 5 Optimization and Simulation Modeling 597 13 Introduction to Optimization Modeling 599 14 Optimization Models 661 15 Introduction to Simulation Modeling 759 16 Simulation Models 829

Part 6 Advanced Data Analysis 895 17 Data Mining 897

Introduction to Spreadsheet Modeling (only in MindTap)

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Brief Contents vii

Part 7 Bonus Online Material* 18-1 18 Importing Data into Excel 18-3 19 Analysis of Variance and Experimental Design 19-1 20 Statistical Process Control 20-1 Appendix A Statistical Reporting A-1

•Bonus Online Material for this text can be found on the text companion website at cengagebrain.com.

References 943 Index 945

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viii

Contents

Preface xviii

1 Introduction to Business Analytics 1 1-1 Introduction 3 1-2 Overview of the Book 4

1-2a The Methods 4 1-2b The Software 7

1-3 Modeling and Models 10 1-3a Graphical Models 10 1-3b Algebraic Models 11 1-3c Spreadsheet Models 12 1-3d A Seven-Step Modeling Process 13

1-4 Conclusion 15

PART 1 EXPLORING DATA 17

2 Describing the Distribution of a Single Variable 19 2-1 Introduction 21 2-2 Basic Concepts 22

2-2a Populations and Samples 22 2-2b Data Sets, Variables, and Observations 23 2-2c Types of Data 24

2-3 Descriptive Measures for Categorical Variables 26 2-4 Descriptive Measures for Numerical Variables 30

2-4a Numerical Summary Measures 31 2-4b Numerical Summary Measures with StatTools 40 2-4c Analysis ToolPak Add-In 45 2-4d Charts for Numerical Variables 45

2-5 Time Series Data 54 2-6 Outliers and Missing Values 61

2-6a Outliers 61 2-6b Missing Values 61

2-7 Excel Tables for Filtering, Sorting, and Summarizing 63 2-8 Conclusion 71

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Contents ix

3 Finding Relationships among Variables 79 3-1 Introduction 80 3-2 Relationships among Categorical Variables 82 3-3 Relationships among Categorical Variables and a Numerical Variable 86

3-3a Stacked and Unstacked Formats 86 3-4 Relationships among Numerical Variables 95

3-4a Scatterplots 95 3-4b Correlation and Covariance 101

3-5 Pivot Tables 108 3-6 Conclusion 131

PART 2 PROBABILITY AND DECISION MAKING UNDER UNCERTAINTY 137

4 Probability and Probability Distributions 139 4-1 Introduction 140 4-2 Probability Essentials 142

4-2a Rule of Complements 142 4-2b Addition Rule 142 4-2c Conditional Probability and the Multiplication Rule 143 4-2d Probabilistic Independence 146 4-2e Equally Likely Events 147 4-2f Subjective Versus Objective Probabilities 147

4-3 Probability Distribution of a Single Random Variable 150 4-3a Summary Measures of a Probability Distribution 151 4-3b Conditional Mean and Variance 154

4-4 Introduction to Simulation 156 4-5 Conclusion 160

5 Normal, Binomial, Poisson, and Exponential Distributions 166 5-1 Introduction 167 5-2 The Normal Distribution 168

5-2a Continuous Distributions and Density Functions 168 5-2b The Normal Density 169 5-2c Standardizing: Z-ValuesZ-ValuesZ 170 5-2d Normal Tables and Z-ValuesZ-ValuesZ 172 5-2e Normal Calculations in Excel 174 5-2f5-2f Empirical Rules Revisited 177 5-2g Weighted Sums of Normal Random Variables 177

5-3 Applications of the Normal Distribution 178

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x Contents

5-4 The Binomial Distribution 190 5-4a Mean and Standard Deviation of the Binomial Distribution 193 5-4b The Binomial Distribution in the Context of Sampling 193 5-4c The Normal Approximation to the Binomial 194

5-5 Applications of the Binomial Distribution 195 5-6 The Poisson and Exponential Distributions 207

5-6a The Poisson Distribution 207 5-6b The Exponential Distribution 210

5-7 Conclusion 212

6 Decision Making under Uncertainty 222 6-1 Introduction 223 6-2 Elements of Decision Analysis 225

6-2a Identifying the Problem 225 6-2b Possible Decisions 226 6-2c Possible Outcomes 226 6-2d Probabilities of Outcomes 226 6-2e Payoffs and Costs 227 6-2f6-2f Decision Criterion 227 6-2g More about the EMV Criterion 228 6-2h Decision Trees 230

6-3 One-Stage Decision Problems 232 6-4 The PrecisionTree Add-In 236 6-5 Multistage Decision Problems 239 6-6 The Role of Risk Aversion 257

6-6a Utility Functions 258 6-6b Exponential Utility 259 6-6c Certainty Equivalents 262 6-6d Is Expected Utility Maximization Used? 263

6-7 Conclusion 264

PART 3 STATISTICAL INFERENCE 277

7 Sampling and Sampling Distributions 279 7-1 Introduction 280 7-2 Sampling Terminology 280 7-3 Methods for Selecting Random Samples 282

7-3a Simple Random Sampling 282 7-3b Systematic Sampling 287 7-3c Stratified Sampling 288 7-3d Cluster Sampling 289 7-3e Multistage Sampling Schemes 290

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Contents xi

7-4 Introduction to Estimation 292 7-4a Sources of Estimation Error 292 7-4b Key Terms in Sampling 293 7-4c Sampling Distribution of the Sample Mean 295 7-4d The Central Limit Theorem 299 7-4e Sample Size Selection 304 7-4f7-4f Summary of Key Ideas for Simple Random Sampling 305

7-5 Conclusion 307

8 Confidence Interval Estimation 311 8-1 Introduction 312 8-2 Sampling Distributions 314

8-2a The t Distributiont Distributiont 314 8-2b Other Sampling Distributions 317

8-3 Confidence Interval for a Mean 317 8-4 Confidence Interval for a Total 324 8-5 Confidence Interval for a Proportion 326 8-6 Confidence Interval for a Standard Deviation 331 8-7 Confidence Interval for the Difference between Means 335

8-7a Independent Samples 335 8-7b Paired Samples 339

8-8 Confidence Interval for the Difference between Proportions 342 8-9 Sample Size Selection 344

8-9a Sample Size Selection for Estimation of the Mean 345 8-9b Sample Size Selection for Estimation of Other Parameters 347

8-10 Conclusion 352

9 Hypothesis Testing 363 9-1 Introduction 364 9-2 Concepts in Hypothesis Testing 365

9-2a Null and Alternative Hypotheses 366 9-2b One-Tailed Versus Two-Tailed Tests 366 9-2c Types of Errors 367 9-2d Significance Level and Rejection Region 368 9-2e Significance from p-valuesp-valuesp 368 9-2f Type II Errors and Power 370 9-2g Hypothesis Tests and Confidence Intervals 371 9-2h Practical versus Statistical Significance 371

9-3 Hypothesis Tests for a Population Mean 372 9-4 Hypothesis Tests for Other Parameters 377

9-4a Hypothesis Tests for a Population Proportion 377 9-4b Hypothesis Tests for Differences between Population Means 379

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xii Contents

9-4c Hypothesis Test for Equal Population Variances 387 9-4d Hypothesis Tests for Differences between Population Proportions 388

9-5 Tests for Normality 395 9-6 Chi-Square Test for Independence 401 9-7 Conclusion 406

PART 4 REGRESSION ANALYSIS AND TIME SERIES FORECASTING 415

10 Regression Analysis: Estimating Relationships 417 10-1 Introduction 418 10-2 Scatterplots: Graphing Relationships 421

10-2a Linear versus Nonlinear Relationships 426 10-2b Outliers 426 10-2c Unequal Variance 427 10-2d No Relationship 427

10-3 Correlations: Indicators of Linear Relationships 428 10-4 Simple Linear Regression 430

10-4a Least Squares Estimation 430 10-4b Standard Error of Estimate 438 10-4c The Percentage of Variation Explained: R-Square 440

10-5 Multiple Regression 443 10-5a Interpretation of Regression Coefficients 443 10-5b Interpretation of Standard Error of Estimate and R-Square 446

10-6 Modeling Possibilities 449 10-6a Dummy Variables 450 10-6b Interaction Variables 456 10-6c Nonlinear Transformations 460

10-7 Validation of the Fit 470 10-8 Conclusion 472

11 Regression Analysis: Statistical Inference 482 11-1 Introduction 484 11-2 The Statistical Model 484 11-3 Inferences about the Regression Coefficients 488

11-3a Sampling Distribution of the Regression Coefficients 489 11-3b Hypothesis Tests for the Regression Coefficients and p-Valuesp-Valuesp 491 11-3c A Test for the Overall Fit: The ANOVA Table 492

11-4 Multicollinearity 496 11-5 Include/Exclude Decisions 502 11-6 Stepwise Regression 507 11-7 Outliers 512

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Contents xiii

11-8 Violations of Regression Assumptions 517 11-8a Nonconstant Error Variance 517 11-8b Nonnormality of Residuals 518 11-8c Autocorrelated Residuals 519

11-9 Prediction 521 11-10 Conclusion 527

12 Time Series Analysis and Forecasting 539 12-1 Introduction 540 12-2 Forecasting Methods: An Overview 541

12-2a Extrapolation Models 541 12-2b Econometric Models 542 12-2c Combining Forecasts 543 12-2d Components of Time Series Data 543 12-2e Measures of Accuracy 546

12-3 Testing for Randomness 548 12-3a The Runs Test 550 12-3b Autocorrelation 552

12-4 Regression-Based Trend Models 556 12-4a Linear Trend 556 12-4b Exponential Trend 559

12-5 The Random Walk Model 562 12-6 Moving Averages Forecasts 565 12-7 Exponential Smoothing Forecasts 570

12-7a Simple Exponential Smoothing 571 12-7b Holt’s Model for Trend 575

12-8 Seasonal Models 580 12-8a Winters’ Exponential Smoothing Model 581 12-8b Deseasonalizing: The Ratio-to-Moving-Averages Method 584 12-8c Estimating Seasonality with Regression 585

12-9 Conclusion 590

PART 5 OPTIMIZATION AND SIMULATION MODELING 597

13 Introduction to Optimization Modeling 599 13-1 Introduction 600 13-2 Introduction to Optimization 601 13-3 A Two-Variable Product Mix Model 602 13-4 Sensitivity Analysis 615

13-4a Solver’s Sensitivity Report 616 13-4b SolverTable Add-In 619 13-4c Comparison of Solver’s Sensitivity Report and SolverTable 626

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xiv Contents

13-5 Properties of Linear Models 626 13-6 Infeasibility and Unboundedness 629 13-7 A Larger Product Mix Model 631 13-8 A Multiperiod Production Model 640 13-9 A Comparison of Algebraic and Spreadsheet Models 649 13-10 A Decision Support System 750 13-11 Conclusion 652

14 Optimization Models 661 14-1 Introduction 662 14-2 Employee Scheduling Models 663 14-3 Blending Models 670 14-4 Logistics Models 676

14-4a Transportation Models 677 14-4b Other Logistics Models 685

14-5 Aggregate Planning Models 693 14-6 Financial Models 703 14-7 Integer Optimization Models 714

14-7a Capital Budgeting Models 714 14-7b Fixed-Cost Models 720 14-7c Set-Covering Models 729

14-8 Nonlinear Optimization Models 735 14-8a Basic Ideas of Nonlinear Optimization 735 14-8b Managerial Economics Models 736 14-8c Portfolio Optimization Models 740

14-9 Conclusion 749

15 Introduction to Simulation Modeling 759 15-1 Introduction 760 15-2 Probability Distributions for Input Variables 762

15-2a Types of Probability Distributions 763 15-2b Common Probability Distributions 766 15-2c Using @RISK to Explore Probability Distributions 770

15-3 Simulation and the Flaw of Averages 780 15-4 Simulation with Built-in Excel Tools 783 15-5 Introduction to @RISK 794

15-5a @RISK Features 795 15-5b Loading @RISK 795 15-5c @RISK Models with a Single Random Input Variable 796 15-5d Some Limitations of @RISK 806 15-5e @RISK Models with Several Random Input Variables 806

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Contents xv

15-6 The Effects of Input Distributions on Results 811 15-6a Effect of the Shape of the Input Distribution(s) 812 15-6b Effect of Correlated Input Variables 815

15-7 Conclusion 820

16 Simulation Models 829 16-1 Introduction 831 16-2 Operations Models 831

16-2a Bidding for Contracts 831 16-2b Warranty Costs 835 16-2c Drug Production with Uncertain Yield 840

16-3 Financial Models 847 16-3a Financial Planning Models 847 16-3b Cash Balance Models 852 16-3c Investment Models 857

16-4 Marketing Models 864 16-4a Models of Customer Loyalty 864 16-4b Marketing and Sales Models 872

16-5 Simulating Games of Chance 879 16-5a Simulating the Game of Craps 879 16-5b Simulating the NCAA Basketball Tournament 882

16-6 Conclusion 885

PART 6 ADVANCED DATA ANALYSIS 895

17 Data Mining 897 17-1 Introduction 898 17-2 Data Exploration and Visualization 900

17-2a Introduction to Relational Databases 900 17-2b Online Analytical Processing (OLAP) 901 17-2c Power Pivot and Self-Service BI Tools in Excel 904 17-2d Visualization Software 911

17-3 Classification Methods 912 17-3a Logistic Regression 913 17-3b Neural Networks 918 17-3c Naïve Bayes 923 17-3d Classification Trees 926 17-3e Measures of Classification Accuracy 927 17-3f17-3f Classification with Rare Events 930

17-4 Clustering 933 17-5 Conclusion 938

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xvi Contents

PART 7 BONUS ONLINE MATERIAL 18-1

18 Importing Data into Excel 18-3 18-1 Introduction 18-4 18-2 Rearranging Excel Data 18-5 18-3 Importing Text Data 18-9 18-4 Importing Data into Excel 18-15

18-4a Importing from Access with Old Tools 18-15 18-4b Importing from Access with Power Query 18-16 18-4c Using Microsoft Query 18-18 18-4d SQL Statements and M 18-26 18-4e Web Queries 18-26

18-5 Cleansing Data 18-28 18-6 Conclusion 18-35

19 Analysis of Variance and Experimental Design 19-1 19-1 Introduction 19-2 19-2 One-Way ANOVA 19-5

19-2a The Equal-Means Test 19-5 19-2b Confidence Intervals for Differences between Means 19-8 19-2c Using a Logarithmic Transformation 19-11

19-3 Using Regression to Perform ANOVA 19-17 19-4 The Multiple Comparison Problem 19-20 19-5 Two-Way ANOVA 19-24

19-5a Confidence Intervals for Contrasts 19-31 19-5b Assumptions of Two-Way ANOVA 19-34

19-6 More about Experimental Design 19-35 19-6a Randomization 19-36 19-6b Blocking 19-38 19-6c Incomplete Designs 19-42

19-7 Conclusion 19-45

20 Statistical Process Control 20-1 20-1 Introduction 20-3 20-2 Deming’s 14 Points 20-4 20-3 Introduction to Control Charts 20-7 20-4 Control Charts for Variables 20-9

20-4a Control Charts and Hypothesis Testing 20-15 20-4b Other Out-of-Control Indications 20-16 20-4c Rational Subsamples 20-17 20-4d Deming’s Funnel Experiment and Tampering 20-20 20-4e Control Charts in the Service Industry 20-23

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Contents xvii

20-5 Control Charts for Attributes 20-27 20-5a The p Chartp Chartp 20-27 20-5b The Red Bead Experiment 20-31

20-6 Process Capability 20-34 20-6a Process Capability Indexes 20-37 20-6b More on Motorola and 6-sigma 20-42

20-7 Conclusion 20-45

Appendix A: Statistical Reporting A-1 A-1 Introduction A-1 A-2 Suggestions for Good Statistical Reporting A-2

A-2a Planning A-2 A-2b Developing a Report A-3 A-2c Be Clear A-4 A-2d Be Concise A-5 A-2e Be Precise A-5

A-3 Examples of Statistical Reports A-7 A-4 Conclusion A-18

References 943

Index 945

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xviii

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