Statistical Quality Control

PART 1 INTRODUCTION 1 1MODERN QUALITY MANAGEMENT AND IMPROVEMENT 3 Chapter Overview and Learning Objectives 3 1.1 The Meaning of Quality and Quality Improvement 4 1.1.1 Dimensions of Quality 4 1.1.2 Quality Engineering Terminology 8 1.2 A Brief History of Quality Control and Improvement 9 1.3 Statistical Methods for Quality Control and Improvement 13 1.4 Management Aspects of Quality Improvement 16 1.4.1 Quality Philosophy and Management Strategies 17 1.4.2 The Link Between Quality and Productivity 35 1.4.3 Supply Chain Quality Management 36 1.4.4 Quality Costs 38 1.4.5 Legal Aspects of Quality 44 1.4.6 Implementing Quality Improvement 45 2 THE DMAIC PROBLEM SOLVING PROCESS 48 Chapter Overview and Learning Objectives 48 2.1 Overview of DMAIC 49 2.2 The Define Step 52 2.3 The Measure Step 54 2.4 The Analyze Step 55 2.5 The Improve Step 56 2.6 The Control Step 57 2.7 Examples of DMAIC 57 2.7.1 Litigation Documents 57 2.7.2 Improving On-Time Delivery 59 2.7.3 Improving Service Quality in a Bank 62 PART 2 STATISTICAL METHODS USEFUL IN QUALITY CONTROL AND IMPROVEMENT 65 3 STATISTICAL MODELS OR QUALITY CONTROL AND IMPROVEMENT 67 Chapter Overview and Learning Objectives 68 3.1 Describing Variation 68 3.1.1 The Stem-and-Leaf Plot 68 3.1.2 The Histogram 70 3.1.3 Numerical Summary of Data 73 3.1.4 The Box Plot 75 3.1.5 Probability Distributions 76 3.2 Important Discrete Distributions 80 3.2.1 The Hypergeometric Distribution 80 3.2.2 The Binomial Distribution 81 3.2.3 The Poisson Distribution 83 3.2.4 The Negative Binomial and Geometric Distributions 86 3.3 Important Continuous Distributions 88 3.3.1 The Normal Distribution 88 3.3.2 The Lognormal Distribution 90 3.3.3 The Exponential Distribution 92 3.3.4 The Gamma Distribution 93 3.3.5 The Weibull Distribution 95 3.4 Probability Plots 97 3.4.1 Normal Probability Plots 97 3.4.2 Other Probability Plots 99 3.5 Some Useful Approximations 100 3.5.1 The Binomial Approximation to the Hypergeometric 100 3.5.2 The Poisson Approximation to the Binomial 100 3.5.3 The Normal Approximation to the Binomial 101 3.5.4 Comments on Approximations 102 4STATISTICAL INFERENCE IN QUALITY CONTROL AND IMPROVEMENT 108 Chapter Overview and Learning Objectives 109 4.1 Statistics and Sampling Distributions 110 4.1.1 Sampling from a Normal Distribution 111 4.1.2 Sampling from a Bernoulli Distribution 113 4.1.3 Sampling from a Poisson Distribution 114 4.2 Point Estimation of Process Parameters 115 4.3 Statistical Inference for a Single Sample 117 4.3.1 Inference on the Mean of a Population, Variance Known 118 4.3.2 The Use of P-Values for Hypothesis Testing 121 4.3.3 Inference on the Mean of a Normal Distribution, Variance Unknown 122 4.3.4 Inference on the Variance of a Normal Distribution 126 4.3.5 Inference on a Population Proportion 128 4.3.6 The Probability of Type II Error and Sample Size Decisions 130 4.4 Statistical Inference for Two Samples 133 4.4.1 Inference for a Difference in Means, Variances Known 134 4.4.2 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 136 4.4.3 Inference on the Variances of Two Normal Distributions 143 4.4.4 Inference on Two Population Proportions 145 4.5 What If There Are More Than Two Populations? The Analysis of Variance 146 4.5.1 An Example 146 4.5.2 The Analysis of Variance 148 4.5.3 Checking Assumptions: Residual Analysis 154 4.6 Linear Regression Models 156 4.6.1 Estimation of the Parameters in Linear Regression Models 157 4.6.2 Hypothesis Testing in Multiple Regression 163 4.6.3 Confidance Intervals in Multiple Regression 169 4.6.4 Prediction of New Observations 170 4.6.5 Regression Model Diagnostics 171 PART 3 BASIC METHODS OF STATISTICAL PROCESS CONTROL AND CAPABILITY ANALYSIS 185 5HOW SPC WORKS 187 Chapter Overview and Learning Objectives 187 5.1 Introduction 188 5.2 Chance and Assignable Causes of Quality Variation 189 5.3 Statistical Basis of the Control Chart 190 5.3.1 Basic Principles 190 5.3.2 Choice of Control Limits 197 5.3.3 Sample Size and Sampling Frequency 199 5.3.4 Rational Subgroups 201 5.3.5 Analysis of Patterns on Control Charts 203 5.3.6 Discussion of Sensitizing Rules for Control Charts 205 5.3.7 Phase I and Phase II of Control Chart Application 206 5.4 The Rest of the Magnificent Seven 207 5.5 Implementing SPC in a Quality Improvement Program 213 5.6 An Application of SPC 214 5.7 Applications of Statistical Process Control and Quality Improvement Tools in Transactional and Service Businesses 221 6VARIABLES CONTROL CHARTS 234 Chapter Overview and Learning Objectives 235 6.1 Introduction 235 6.2 Control Charts for --x and R 236 6.2.1 Statistical Basis of the Charts 236 6.2.2 Development and Use of --x and R Charts 239 6.2.3 Charts Based on Standard Values 250 6.2.4 Interpretation of --x and R Charts 251 6.2.5 The Effect of Nonnormality on --x and R Charts 254 6.2.6 The Operating-Characteristic Function 254 6.2.7 The Average Run Length for the --x Chart 257 6.3 Control Charts for --x and s 259 6.3.1 Construction and Operation of --x and s Charts 259 6.3.2 The --x and s Control Charts with Variable Sample Size 263 6.3.3 The s2 Control Chart 267 6.4 The Shewhart Control Chart for Individual Measurements 267 6.5 Summary of Procedures for --x , R, and s Charts 276 6.6 Applications of Variables Control Charts 276 7ATTRIBUTES CONTROL CHARTS 297 Chapter Overview and Learning Objectives 297 7.1 Introduction 298 7.2 The Control Chart for Fraction Nonconforming 299 7.2.1 Development and Operation of the Control Chart 299 7.2.2 Variable Sample Size 310 7.2.3 Applications in Transactional and Service Businesses 315 7.2.4 The Operating-Characteristic Function and Average Run Length Calculations 315 7.3 Control Charts for Nonconformities (Defects) 317 7.3.1 Procedures with Constant Sample Size 318 7.3.2 Procedures with Variable Sample Size 328 7.3.3 Demerit Systems 330 7.3.4 The Operating-Characteristic Function 331 7.3.5 Dealing with Low Defect Levels 332 7.3.6 Nonmanufacturing Applications 335 7.4 Choice Between Attributes and Variables Control Charts 335 7.5 Guidelines for Implementing Control Charts 339 8DETERMINING PROCESS AND MEASUREMENT SYSTEMS CAPABILITY 355 Chapter Overview and Learning Objectives 356 8.1 Introduction 356 8.2 Process Capability Analysis Using a Histogram or a Probability Plot 358 8.2.1 Using the Histogram 358 8.2.2 Probability Plotting 360 8.3 Process Capability Ratios 362 8.3.1 Use and Interpretation of Cp 362 8.3.2 Process Capability Ratio for an Off-Center Process 365 8.3.3 Normality and the Process Capability Ratio 367 8.3.4 More about Process Centering 368 8.3.5 Confidence Intervals and Tests on Process Capability Ratios 370 8.4 Process Capability Analysis Using a Control Chart 375 8.5 Process Capability Analysis Using Designed Experiments 377 8.6 Process Capability Analysis with Attribute Data 378 8.7 Gauge and Measurement System Capability Studies 379 8.7.1 Basic Concepts of Gauge Capability 379 8.7.2 The Analysis of Variance Method 384 8.7.3 Confidence Intervals in Gauge R & R Studies 387 8.7.4 False Defectives and Passed Defectives 388 8.7.5 Attribute Gauge Capability 392 8.7.6 Comparing Customer and Supplier Measurement Systems 394 8.8 Setting Specification Limits on Discrete Components 396 8.8.1 Linear Combinations 397 8.8.2 Nonlinear Combinations 400 8.9 Estimating the Natural Tolerance Limits of a Process 401 8.9.1 Tolerance Limits Based on the Normal Distribution 402 8.9.2 Nonparametric Tolerance Limits 403 PART 4 OTHER STATISTICAL PROCESSMONITORING AND CONTROL TECHNIQUES 411 9TIME-WEIGHTED CONTROL CHARTS 413 Chapter Overview and Learning Objectives 414 9.1 The Cumulative Sum Control Chart 414 9.1.1 Basic Principles: The CUSUM Control Chart for Monitoring the Process Mean 414 9.1.2 The Tabular or Algorithmic CUSUM for Monitoring the Process Mean 417 9.1.3 Recommendations for CUSUM Design 422 9.1.4 The Standardized CUSUM 424 9.1.5 Improving CUSUM Responsiveness for Large Shifts 424 9.1.6 The Fast Initial Response or Headstart Feature 424 9.1.7 One-Sided CUSUMs 427 9.1.8 A CUSUM for Monitoring Process Variability 427 9.1.9 Rational Subgroups 428 9.1.10 CUSUMs for Other Sample Statistics 428 9.1.11 The V-Mask Procedure 429 9.1.12 The Self-Starting CUSUM 431 9.2 The Exponentially Weighted Moving Average Control Chart 433 9.2.1 The Exponentially Weighted Moving Average Control Chart for Monitoring the Process Mean 433 9.2.2 Design of an EWMA Control Chart 436 9.2.3 Robustness of the EWMA to Nonnormality 438 9.2.4 Rational Subgroups 439 9.2.5 Extensions of the EWMA 439 9.3 The Moving Average Control Chart 442 10ADVANCED CONTROL CHARTING TECHNIQUES 448 Chapter Overview and Learning Objectives 449 10.1 Statistical Process Control for Short Production Runs 450 10.1.1 --x and R Charts for Short Production Runs 450 10.1.2 Attributes Control Charts for Short Production Runs 452 10.1.3 Other Methods 452 10.2 Modified and Acceptance Control Charts 454 10.2.1 Modified Control Limits for the --x Chart 454 10.2.2 Acceptance Control Charts 457 10.3 Control Charts for Multiple-Stream Processes 458 10.3.1 Multiple-Stream Processes 458 10.3.2 Group Control Charts 458 10.3.3 Other Approaches 460 10.4 SPC With Autocorrelated Process Data 461 10.4.1 Sources and Effects of Autocorrelation in Process Data 461 10.4.2 Model-Based Approaches 465 10.4.3 A Model-Free Approach 473 10.5 Adaptive Sampling Procedures 477 10.6 Economic Design of Control Charts 478 10.6.1 Designing a Control Chart 478 10.6.2 Process Characteristics 479 10.6.3 Cost Parameters 479 10.6.4 Early Work and Semieconomic Designs 481 10.6.5 An Economic Model of the ----x Control Chart 482 10.6.6 Other Work 487 10.7 Cuscore Charts 488 10.8 The Changepoint Model for Process Monitoring 490 10.9 Profile Monitoring 491 10.10 Control Charts in Health Care Monitoring and Public Health Surveillance 496 10.11 Overview of Other Procedures 497 10.11.1 Tool Wear 497 10.11.2 Control Charts Based on Other Sample Statistics 498 10.11.3 Fill Control Problems 498 10.11.4 Precontrol 499 10.11.5 Tolerance Interval Control Charts 500 10.11.6 Monitoring Processes with Censored Data 501 10.11.7 Monitoring Bernoulli Processes 501 10.11.8 Nonparametric Control Charts 502 11MULTIVARIATE SPC 509 Chapter Overview and Learning Objectives 509 11.1 The Multivariate Quality-Control Problem 510 11.2 Description of Multivariate Data 512 11.2.1 The Multivariate Normal Distribution 512 11.2.2 The Sample Mean Vector and Covariance Matrix 513 11.3 The Hotelling T2 Control Chart 514 11.3.1 Subgrouped Data 514 11.3.2 Individual Observations 521 11.4 The Multivariate EWMA Control Chart 524 11.5 Regression Adjustment 528 11.6 Control Charts for Monitoring Variability 531 11.7 Latent Structure Methods 533 11.7.1 Principal Components 533 11.7.2 Partial Least Squares 538 12PROCESS ADJUSTMENT AND PROCESS MONITORING 542 Chapter Overview and Learning Objectives 542 12.1 Process Monitoring and Process Regulation 543 12.2 Process Control by Feedback Adjustment 544 12.2.1 A Simple Adjustment Scheme: Integral Control 544 12.2.2 The Adjustment Chart 549 12.2.3 Variations of the Adjustment Chart 551 12.2.4 Other Types of Feedback Controllers 554 12.3 Combining SPC and EPC 555 PART 5 PROCESS DESIGN AND IMPROVEMENT WITH DESIGNED EXPERIMENTS 561 13BASIC EXPERIMENTAL DESIGN FOR PROCESS IMPROVEMENT 563 Chapter Overview and Learning Objectives 564 13.1 What is Experimental Design? 564 13.2 Examples of Designed Experiments In Process and Product Improvement 566 13.3 Guidelines for Designing Experiments 568 13.4 Factorial Experiments 570 13.4.1 An Example 572 13.4.2 Statistical Analysis 572 13.4.3 Residual Analysis 577 13.5 The 2k Factorial Design 578 13.5.1 The 22 Design 578 13.5.2 The 2k Design for k => 3 Factors 583 13.5.3 A Single Replicate of the 2k Design 593 13.5.4 Addition of Center Points to the 2k Design 596 13.5.5 Blocking and Confounding in the 2k Design 599 13.6 Fractional Replication of the 2k Design 601 13.6.1 The One-Half Fraction of the 2k Design 601 13.6.2 Smaller Fractions: The 2k--p Fractional Factorial Design 606 14PROCESS OPTIMIZATION 617 Chapter Overview and Learning Objectives 617 14.1 Response Surface Methods and Designs 618 14.1.1 The Method of Steepest Ascent 620 14.1.2 Analysis of a Second-Order Response Surface 622 14.2 Process Robustness Studies 626 14.2.1 Background 626 14.2.2 The Response Surface Approach to Process Robustness Studies 628 14.3 Evolutionary Operation 634 PART 6 ACCEPTANCE SAMPLING 647 15BASIC ACCEPTANCE SAMPLING PROCEDURES 649 Chapter Overview and Learning Objectives 649 15.1 The Acceptance-Sampling Problem 650 15.1.1 Advantages and Disadvantages of Sampling 651 15.1.2 Types of Sampling Plans 652 15.1.3 Lot Formation 653 15.1.4 Random Sampling 653 15.1.5 Guidelines for Using Acceptance Sampling 654 15.2 Single-Sampling Plans for Attributes 655 15.2.1 Definition of a Single-Sampling Plan 655 15.2.2 The OC Curve 655 15.2.3 Designing a Single-Sampling Plan with a Specified OC Curve 660 15.2.4 Rectifying Inspection 661 15.3 Double, Multiple, and Sequential Sampling 664 15.3.1 Double-Sampling Plans 665 15.3.2 Multiple-Sampling Plans 669 15.3.3 Sequential-Sampling Plans 670 15.4 Military Standard 105E (ANSI/ASQC Z1.4, ISO 2859) 673 15.4.1 Description of the Standard 673 15.4.2 Procedure 675 15.4.3 Discussion 679 15.5 The Dodge--Romig Sampling Plans 681 15.5.1 AOQL Plans 682 15.5.2 LTPD Plans 685 15.5.3 Estimation of Process Average 685 16ADDITIONAL SAMPLING PROCEDURES 688 Chapter Overview and Learning Objectives 688 16.1 Acceptance Sampling by Variables 689 16.1.1 Advantages and Disadvantages of Variables Sampling 689 16.1.2 Types of Sampling Plans Available 690 16.1.3 Caution in the Use of Variables Sampling 691 16.2 Designing a Variables Sampling Plan with a Specified OC Curve 691 16.3 MIL STD 414 (ANSI/ASQC Z1.9) 694 16.3.1 General Description of the Standard 694 16.3.2 Use of the Tables 695 16.3.3 Discussion of MIL STD 414 and ANSI/ASQC Z1.9 697 16.4 Other Variables Sampling Procedures 698 16.4.1 Sampling by Variables to Give Assurance Regarding the Lot or Process Mean 698 16.4.2 Sequential Sampling by Variables 699 16.5 Chain Sampling 699 16.6 Continuous Sampling 701 16.6.1 CSP-1 701 16.6.2 Other Continuous-Sampling Plans 704 16.7 Skip-Lot Sampling Plans 704 APPENDIX 709 I. Summary of Common Probability Distributions Often Used in Statistical Quality Control 710 II. Cumulative Standard Normal Distribution 711 III. Percentage Points of the chi2 Distribution 713 IV. Percentage Points of the t Distribution 714 V. Percentage Points of the F Distribution 715 VI. Factors for Constructing Variables Control Charts 720 VII. Factors for Two-Sided Normal Tolerance Limits 721 VIII. Factors for One-Sided Normal Tolerance Limits 722 BIBLIOGRAPHY 723 ANSWERS TO SELECTED EXERCISES 739 INDEX 749