Statistics, Data Analysis, and Decision Modeling

Transcription

1 - ' 'li* Statistics, Data Analysis, and Decision Modeling T H I R D E D I T I O N James R. Evans University of Cincinnati PEARSON Prentice Hall Upper Saddle River, New Jersey 07458

2 CONTENTS Preface xv PART I: STATISTICS AND DATA ANALYSIS CHAPTER 1 Data and Business Decisions 3 Statistical Thinking in Business 5 Six Sigma and Statistical Thinking 6 Data in the Business Environment 7 Metrics and Measurement 8 The Balanced Scorecard 10 Sources and Types of Data 11 Data Classification 12 Populations, Samples, and Statistics 15 Using Microsoft Excel 17 Basic Excel Skills 17 Copying Formulas and Cell References 17 Functions 19 Other Useful Excel Tips 21 Excel Add-lns 22 Working with Data in Excel 24 PivotTables 24 Conceptual Review Questions 31 Problems and Exercises 31 Case: The Tracway Balanced Scorecard 32 CHAPTER 2 Displaying and Summarizing Data 37 Displaying Data with Charts and Graphs 38 Column and Bar Charts 39 Line Charts 4.2 Pie Charts 43 Area Charts 43 Scatter Diagrams 44 Miscellaneous Excel Charts 45 Summary of Graphical Display Methods 45 Contingency Tables and Cross Tabulations 47 Descriptive Statistics 47 Frequency Distributions and Histograms 49 Measures of Central Tendency 51 Measures of Dispersion 54 Importance of the Standard Deviation 56 Calculations for Grouped Data 57 VII

3 Coefficient of Variation 58 Measures of Shape 59 Excel's Descriptive Statistics Tool 61 Data Profiles and Proportions 62 Proportions 64 Visual Display of Statistical Measures 64 Box-and-Whisker Plots 64 Stem-and-Leaf Displays 66 Dot Scale Diagrams 68 Statistical Relationships 69 Case Study: Using Descriptive Statistics for the Malcolm Baldrige National Quality Award 72 Conceptual Review Questions 75 Problems and Exercises 75 Case: Descriptive Statistical Analysis of Tracway Data 81 CHAPTER 3 Random Variables and Probability Distributions 82 Basic Concepts 83 Probability 83 Probability Rules and Calculations 84 Conditional Probability 86 Statistical Independence 87 Bayes's Theorem 88 Random Variables and Probability Distributions 89 Discrete Probability Distributions 89 Continuous Probability Distributions 91 Expected Value and Variance of a Random Variable 95 Discrete Probability Distributions 96 Bernoulli and Binomial Distributions 96 Poisson Distribution 99 Continuous Probability Distributions 101 Uniform Distribution 101 Normal Distribution 102 Triangular Distribution 106 Exponential Distribution 108 Other Useful Distributions 109 Probability Distributions in PHStat 112 Monte Carlo Methods in Statistics 113 Random Numbers 114 Random Sampling from Probability Distributions 114 Generating Random Vanates in Excel 116 Applications of Monte Carlo Methods in Statistics 118 Sampling Distributions and Sampling Error 120 Standard Error of the Mean 122 Applying Sampling Distributions 123 Conceptual Review Questions 124 Problems and Exercises 124 Case: Probability Modeling for Tracway Quality Measurements 130 viii

4 CHAPTER 4 Sampling and Estimation 131 Statistical Sampling 132 Sample Design 132 Sampling Methods 133 Errors in Sampling 136 Sampling and Estimation 136 Point Estimates 137 Unbiased Estimators 137 Interval Estimates 138 Confidence Intervals for the Mean 139 Confidence Interval for the Mean with Unknown Standard Deviation 142 Sampling and Confidence Intervals from Finite Populations 143 Confidence Intervals for Proportions 145 Confidence Intervals and Sample Size 146 Additional Types of Confidence Intervals 14.7 Population Total 148 Differences Between Means 149 Paired Samples 151 Differences Betiveen Proportions 152 Variance and Standard Deviation 152 Time Series Data 154 Summary and Conclusions About Confidence Intervals 154 Confidence Intervals and Probability Intervals 155 Conceptual Review Questions 156 Problems and Exercises 156 Case: Statistical Inference for Tracway 158 CHAPTER 5 Hypothesis Testing and Statistical Inference 160 Hypothesis Testing 161 Hypothesis Formulation 162 Significance Level 163 Decision Rules 164 One-Sample Hypothesis Tests 167 One-Sample Tests for Means 167 Using p- Values 170 One-Sample Test for Proportions 171 Type II Errors and the Power of a Test 172 Two-Sample Hypothesis Tests 175 Two-Sample Tests for Means 175 Tiuo-Sample Test for Means with Paired Samples 176 Two-Sample Tests for Proportions 178 Hypothesis Tests and Confidence Intervals 178 F-Testfor Differences in Two Variances 178 Anova: Testing Differences of Several Means 180 Assumptions of ANOVA 183 Tukey-Kramer Multiple Comparison Procedure 184 Chi-Square Test for Independence 185 Design of Experiments 187 Factorial Experiments and Tzvo-Way ANOVA 188 Two-Way ANOVA 190 ix

5 Conceptual Review Questions 192 Problems and Exercises 193 Case: Statistical Inference for Tracway 198 CHAPTER 6 Regression Analysis 199 Simple Linear Regression 201 Least-Squares Estimation 202 Application of Regression Analysis to Investment Risk 205 Understanding and Measuring Variation in Regression 206 Coefficient of Determination and Correlation Coefficient 208 Standard Error of the Estimate and Confidence Intervals 208 Prediction Intervals 210 Regression As Analysis of Variance 211 Assumptions of Regression Analysis 214 Multiple Linear Regression 216 Interpreting Results from Multiple Linear Regression 217 Building Good Regression Models 219 Sofhuare Support for Regression Modeling 221 Correlation and Multicollinearity 223 Regression with Categorical Independent Variables 226 Categorical Variables with More Than Two Levels 229 Regression Models with Nonlinear Terms 231 Conceptual Review Questions 234 Problems and Exercises 234 Case: Regression Analysis for Tracway 239 References 240 CHAPTER 7 Forecasting 241 Qualitative and Judgmental Methods 243 Historical Analogy 243 The Delphi Method 243 Applying the Delphi Method 244 Indicators and Indexes 246 Statistical Forecasting Models 247 Forecasting Models for Stationary Time Series 249 Moving Average Models 249 Error Metrics and Forecast Accuracy 251 Exponential Smoothing Models 254 Forecasting Models with Linear Trends 255 Double Moving Average 255 Double Exponential Smoothing 258 Forecasting Models with Seasonality 259 Additive Seasonality 259 Multiplicative Seasonality 261 Models for Time Series with Trend and Seasonal Components 262 Holt-Winters Additive Model 262 Holt-Winters Multiplicative Model 262 CB Predictor 264

6 Regression Models for Forecasting 266 Incorporating Seasonality in Regression Models 269 Causal Regression Forecasting Models 270 The Practice of Forecasting 272 Conceptual Review Questions 274 Problems and Exercises 274 Case: Forecasting for Tracway 277 References 277 CHAPTER 8 Statistical Quality Control 278 The Role of Statistics and Data Analysis in Quality Control 279 Statistical Process Control 280 Control Charts 281 x- and R-charts 282 Analyzing Control Charts 287 Control Charts for Attributes 293 Variable Sample Size 295 Statistical Issues in the Design of Control Charts 298 Process Capability Analysis 298 Conceptual Review Questions 301 Problems and Exercises 301 Case: Quality Control at Tracway 302 References 302 PART II: DECISION MODELING AND ANALYSIS 303 CHAPTER 9 Building and Using Decision Models 305 Decision Models 306 Building Decision Models on Spreadsheets 308 Spreadsheet Quality 311 Model Assumptions 312 Optimization Models 314 Models Involving Uncertainty 315 Characterizing Model Inputs 316 Distribution Fitting 316 Model Analysis 322 Data Tables 322 Tornado and Spider Charts 323 Solving Optimization Models 327 Interpreting and Using Decision Model Results 328 Conceptual Review Questions 329 Problems and Exercises 329 Case: Decision Modeling for Tracway Inventory Management 332 CHAPTER 10 Decisions and Risk 334 Structuring Decision Problems 336 xi

7 Decisions Involving a Single Alternative 336 Decisions Involving Non-Murually Exclusive Alternatives 337 Decisions Involving Mutually Exclusive Alternatives 339 Scoring Models 339 Decisions Involving Uncertainty And Risk 340 Decision Strategies and Risk 341 Understanding Risk in Financial Decisions 343 Expected Value Decision Making 345 Opportunity Loss and Expected Value of Perfect Information 346 Analysis of Portfolio Risk 347 The Newsvendor Problem 34.9 The "Flaw of Averages" 351 Decision Trees 351 Sensitivity Analysis in Decision Trees 358 Utility and Decision Making 359 Exponential Utility Functions 363 Conceptual Review Questions 364 Problems and Exercises 364 Case: A Tracway Decision Problem 373 CHAPTER 11 Risk Analysis and Monte Carlo Simulation 374 Risk Analysis 375 Monte Carlo Simulation with Crystal Ball 376 A Financial Analysis Risk Simulation 376 Specifying Input Information 378 Crystal Ball Outputs 383 Sensitivity Analysis 386 Trend Charts 388 Overlay Charts 388 Crystal Ball Reports and Data Extraction 389 Crystal Ball Functions 389 Saving Crystal Ball Runs 390 Crystal Ball Tools 391 Tornado and Spider Charts 391 Correlation Matrix 391 Bootstrap Tool 392 Other Crystal Ball Tools 394 Applications of Monte Carlo Simulation 395 Retirement Planning 396 Neivsvendor Model 398 Hotel Overbooking 400 Cash Budgeting 403 Project Management 404 Conceptual Review Questions 409 Problems and Exercises 409 Case: Determining a Machine Maintenance Strategy for Tracway 416 CHAPTER 12 Queues and Process Simulation Modeling 417 Queues and Queuing Systems 418 Basic Concepts of Queuing Systems 418 xii

8 Customer Characteristics 419 Service Characteristics 420 Queue Characteristics 421 System Configuration 421 Performance Measures 421 Analytical Queuing Models 422 Single-Server Model 422 Little's Law 424 Process Simulation Concepts 424 Process Simulation with Simquick 426 Queuing Simulation Models 427 Queues in Series with Blocking 432 Grocery Store Checkout Model with Resources 433 Manufacturing Inspection Model with Decision Points 437 Pull System Supply Chain until Exit Schedules 438 Other SimQuick Features and Commercial Simulation Software 440 Continuous Simulation Modeling 442 Conceptual Review Questions 446 Problems and Exercises 446 Case: Tracway Production/Inventory Planning 451 CHAPTER 13 Optimization Modeling 457 Constrained Optimization 458 Types of Optimization Problems 459 Linear Optimization Models 460 Product Mix 462 Media Selection 463 Process Selection 464 Blending 465 Production Planning 466 Cash Management 468 Transportation Problem 469 Spreadsheet Implementation of Linear Programming Models 471 Product Mix Spreadsheet Model 471 Transportation Problem Spreadsheet Model 4.72 Excel Functions to Avoid in Modeling Linear Programs 474 Integer Optimization Models 474 A Cutting Slock Problem 475 Integer Optimization Models with Binary Variables 476 Project Selection 476 Computer Configuration 477 Direct Marketing 480 A Supply Chain Facility Location Model 4.81 Distribution Center Location 482 Nonlinear Optimization 484 Hotel Pricing 484 Markowitz Portfolio Model 486 Conceptual Review Questions 488 Problems and Exercises 488 Case: Distribution Center Location for Tracway 501 : xiii

9 CHAPTER 14 Solving and Analyzing Optimization Models 502 Using Spreadsheet Models for Optimization 503 Solving Linear Optimization Models 504 Solving the Product Mix Model 504 Interpreting Solver Reports 509 How Solver Creates Names in Reports 513 How Solver Handles Lower and Upper Bounds 51.4 Difficulties with Solver 515 Solving Integer Optimization Models 517 Solving Nonlinear Optimization Models 518 Evolutionary Solver for Nonlinear Optimization 521 Risk Analysis and Optimization 522 Combining Optimization and Simulation 524 A Portfolio Allocation Model 525 Using OptQuest 526 Interpreting Results 531 Adding a Requirement 532 Conceptual Review Questions 534 Problems and Exercises 534 Case: Distribution Center Location for Tracway 539 Appendix 540 Table A.I The Cumulative Standard Normal Distribution 541 Table A.2 Critical Values of t 543 Table A.3 Critical Values of x Table A.4 Critical Values of F 547 Table A.5 Critical Values'" 1 of the Studentized Range Q 550 Index 552 xiv

10 CHAPTER 14 Solving and Analyzing Optimization Models 502 Using Spreadsheet Models for Optimization 503 Solving Linear Optimization Models 504 Solving the Product Mix Model 504 Interpreting Solver Reports 509 How Solver Creates Names in Reports 513 How Solver Handles Lower and Upper Bounds 514 Difficulties with Solver 515 Solving Integer Optimization Models 517 Solving Nonlinear Optimization Models 518 Evolutionary Solver for Nonlinear Optimization 521 Risk Analysis and Optimization 522 Combining Optimization and Simulation 524 A Portfolio Allocation Model 525 Using OptQuest 526 Interpreting Results 531 Adding a Requirement 532 Conceptual Review Questions 534 Problems and Exercises 534 Case: Distribution Center Location for Tracway 539 Appendix 540 Table A.I The Cumulative Standard Normal Distribution 541 Table A.2 Critical Values of t 543 Table A.3 Critical Values of x Table A.4 Critical Values of F 547 Table A.5 Critical Values 3 of the Studentized Range Q 550 Index 552 xiv