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by Douglas C. Montgomery
Statistical Quality Control, 7th Edition
Coverpage
Titlepage
Copyright
About the Author
Preface
Contents
PART 1 INTRODUCTION
1 QUALITY IMPROVEMENT IN THE MODERN BUSINESS ENVIRONMENT
Chapter Overview and Learning Objectives
1.1 The Meaning of Quality and Quality Improvement
1.1.1 Dimensions of Quality
1.1.2 Quality Engineering Terminology
1.2 A Brief History of Quality Control and Improvement
1.3 Statistical Methods for Quality Control and Improvement
1.4 Management Aspects of Quality Improvement
1.4.1 Quality Philosophy and Management Strategies
1.4.2 The Link Between Quality and Productivity
1.4.3 Supply Chain Quality Management
1.4.4 Quality Costs
1.4.5 Legal Aspects of Quality
1.4.6 Implementing Quality Improvement
2 THE DMAIC PROCESS
Chapter Overview and Learning Objectives
2.1 Overview of DMAIC
2.2 The Define Step
2.3 The Measure Step
2.4 The Analyze Step
2.5 The Improve Step
2.6 The Control Step
2.7 Examples of DMAIC
2.7.1 Litigation Documents
2.7.2 Improving On-Time Delivery
2.7.3 Improving Service Quality in a Bank
PART 2 STATISTICAL METHODS USEFUL IN QUALITY CONTROL AND IMPROVEMENT
3 MODELING PROCESS QUALITY
Chapter Overview and Learning Objectives
3.1 Describing Variation
3.1.1 The Stem-and-Leaf Plot
3.1.2 The Histogram
3.1.3 Numerical Summary of Data
3.1.4 The Box Plot
3.1.5 Probability Distributions
3.2 Important Discrete Distributions
3.2.1 The Hypergeometric Distribution
3.2.2 The Binomial Distribution
3.2.3 The Poisson Distribution
3.2.4 The Negative Binomial and Geometric Distributions
3.3 Important Continuous Distributions
3.3.1 The Normal Distribution
3.3.2 The Lognormal Distribution
3.3.3 The Exponential Distribution
3.3.4 The Gamma Distribution
3.3.5 The Weibull Distribution
3.4 Probability Plots
3.4.1 Normal Probability Plots
3.4.2 Other Probability Plots
3.5 Some Useful Approximations
3.5.1 The Binomial Approximation to the Hypergeometric
3.5.2 The Poisson Approximation to the Binomial
3.5.3 The Normal Approximation to the Binomial
3.5.4 Comments on Approximations
4 INFERENCES ABOUT PROCESS QUALITY
Chapter Overview and Learning Objectives
4.1 Statistics and Sampling Distributions
4.1.1 Sampling from a Normal Distribution
4.1.2 Sampling from a Bernoulli Distribution
4.1.3 Sampling from a Poisson Distribution
4.2 Point Estimation of Process Parameters
4.3 Statistical Inference for a Single Sample
4.3.1 Inference on the Mean of a Population, Variance Known
4.3.2 The Use of P-Values for Hypothesis Testing
4.3.3 Inference on the Mean of a Normal Distribution, Variance Unknown
4.3.4 Inference on the Variance of a Normal Distribution
4.3.5 Inference on a Population Proportion
4.3.6 The Probability of Type II Error and Sample Size Decisions
4.4 Statistical Inference for Two Samples
4.4.1 Inference for a Difference in Means, Variances Known
4.4.2 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown
4.4.3 Inference on the Variances of Two Normal Distributions
4.4.4 Inference on Two Population Proportions
4.5 What If There Are More Than Two Populations? The Analysis of Variance
4.5.1 An Example
4.5.2 The Analysis of Variance
4.5.3 Checking Assumptions: Residual Analysis
4.6 Linear Regression Models
4.6.1 Estimation of the Parameters in Linear Regression Models
4.6.2 Hypothesis Testing in Multiple Regression
4.6.3 Confidance Intervals in Multiple Regression
4.6.4 Prediction of New Observations
4.6.5 Regression Model Diagnostics
PART 3 BASIC METHODS OF STATISTICAL PROCESS CONTROL AND CAPABILITY ANALYSIS
5 METHODS AND PHILOSOPHY OF STATISTICAL PROCESS CONTROL
Chapter Overview and Learning Objectives
5.1 Introduction
5.2 Chance and Assignable Causes of Quality Variation
5.3 Statistical Basis of the Control Chart
5.3.1 Basic Principles
5.3.2 Choice of Control Limits
5.3.3 Sample Size and Sampling Frequency
5.3.4 Rational Subgroups
5.3.5 Analysis of Patterns on Control Charts
5.3.6 Discussion of Sensitizing Rules for Control Charts
5.3.7 Phase I and Phase II of Control Chart Application
5.4 The Rest of the Magnificent Seven
5.5 Implementing SPC in a Quality Improvement Program
5.6 An Application of SPC
5.7 Applications of Statistical Process Control and Quality Improvement Tools in Transactional and Service Businesses
6 CONTROL CHARTS FOR VARIABLES
Chapter Overview and Learning Objectives
6.1 Introduction
6.2 Control Charts for X and R
6.2.1 Statistical Basis of the Charts
6.2.2 Development and Use of X and R Charts
6.2.3 Charts Based on Standard Values
6.2.4 Interpretation of X and R Charts
6.2.5 The Effect of Nonnormality on X and R Charts
6.2.6 The Operating-Characteristic Function
6.2.7 The Average Run Length for the X Chart
6.3 Control Charts for X and s
6.3.1 Construction and Operation of X and s Charts
6.3.2 The X and s Control Charts with Variable Sample Size
6.3.3 The s2 Control Chart
6.4 The Shewhart Control Chart for Individual Measurements
6.5 Summary of Procedures for X, R, and s Charts
6.6 Applications of Variables Control Charts
7 CONTROL CHARTS FOR ATTRIBUTES
Chapter Overview and Learning Objectives
7.1 Introduction
7.2 The Control Chart for Fraction Nonconforming
7.2.1 Development and Operation of the Control Chart
7.2.2 Variable Sample Size
7.2.3 Applications in Transactional and Service Businesses
7.2.4 The Operating-Characteristic Function and Average Run Length Calculations
7.3 Control Charts for Nonconformities (Defects)
7.3.1 Procedures with Constant Sample Size
7.3.2 Procedures with Variable Sample Size
7.3.3 Demerit Systems
7.3.4 The Operating-Characteristic Function
7.3.5 Dealing with Low Defect Levels
7.3.6 Nonmanufacturing Applications
7.4 Choice Between Attributes and Variables Control Charts
7.5 Guidelines for Implementing Control Charts
8 PROCESS AND MEASUREMENT SYSTEM CAPABILITY ANALYSIS
Chapter Overview and Learning Objectives
8.1 Introduction
8.2 Process Capability Analysis Using a Histogram or a Probability Plot
8.2.1 Using the Histogram
8.2.2 Probability Plotting
8.3 Process Capability Ratios
8.3.1 Use and Interpretation of Cp
8.3.2 Process Capability Ratio for an Off-Center Process
8.3.3 Normality and the Process Capability Ratio
8.3.4 More about Process Centering
8.3.5 Confidence Intervals and Tests on Process Capability Ratios
8.4 Process Capability Analysis Using a Control Chart
8.5 Process Capability Analysis Using Designed Experiments
8.6 Process Capability Analysis with Attribute Data
8.7 Gauge and Measurement System Capability Studies
8.7.1 Basic Concepts of Gauge Capability
8.7.2 The Analysis of Variance Method
8.7.3 Confidence Intervals in Gauge R & R Studies
8.7.4 False Defectives and Passed Defectives
8.7.5 Attribute Gauge Capability
8.7.6 Comparing Customer and Supplier Measurement Systems
8.8 Setting Specification Limits on Discrete Components
8.8.1 Linear Combinations
8.8.2 Nonlinear Combinations
8.9 Estimating the Natural Tolerance Limits of a Process
8.9.1 Tolerance Limits Based on the Normal Distribution
8.9.2 Nonparametric Tolerance Limits
PART 4 OTHER STATISTICAL PROCESS-MONITORING AND CONTROL TECHNIQUES
9 CUMULATIVE SUM AND EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHARTS
Chapter Overview and Learning Objectives
9.1 The Cumulative Sum Control Chart
9.1.1 Basic Principles: The CUSUM Control Chart for Monitoring the Process Mean
9.1.2 The Tabular or Algorithmic CUSUM for Monitoring the Process Mean
9.1.3 Recommendations for CUSUM Design
9.1.4 The Standardized CUSUM
9.1.5 Improving CUSUM Responsiveness for Large Shifts
9.1.6 The Fast Initial Response or Headstart Feature
9.1.7 One-Sided CUSUMs
9.1.8 A CUSUM for Monitoring Process Variability
9.1.9 Rational Subgroups
9.1.10 CUSUMs for Other Sample Statistics
9.1.11 The V-Mask Procedure
9.1.12 The Self-Starting CUSUM
9.2 The Exponentially Weighted Moving Average Control Chart
9.2.1 The Exponentially Weighted Moving Average Control Chart for Monitoring the Process Mean
9.2.2 Design of an EWMA Control Chart
9.2.3 Robustness of the EWMA to Non-normality
9.2.4 Rational Subgroups
9.2.5 Extensions of the EWMA
9.3 The Moving Average Control Chart
10 OTHER UNIVARIATE STATISTICAL PROCESS-MONITORING AND CONTROL TECHNIQUES
Chapter Overview and Learning Objectives
10.1 Statistical Process Control for Short Production Runs
10.1.1 X and R Charts for Short Production Runs
10.1.2 Attributes Control Charts for Short Production Runs
10.1.3 Other Methods
10.2 Modified and Acceptance Control Charts
10.2.1 Modified Control Limits for the X Chart
10.2.2 Acceptance Control Charts
10.3 Control Charts for Multiple-Stream Processes
10.3.1 Multiple-Stream Processes
10.3.2 Group Control Charts
10.3.3 Other Approaches
10.4 SPC With Autocorrelated Process Data
10.4.1 Sources and Effects of Autocorrelation in Process Data
10.4.2 Model-Based Approaches
10.4.3 A Model-Free Approach
10.5 Adaptive Sampling Procedures
10.6 Economic Design of Control Charts
10.6.1 Designing a Control Chart
10.6.2 Process Characteristics
10.6.3 Cost Parameters
10.6.4 Early Work and Semieconomic Designs
10.6.5 An Economic Model of the X Control Chart
10.6.6 Other Work
10.7 Cuscore Charts
10.8 The Changepoint Model for Process Monitoring
10.9 Profile Monitoring
10.10 Control Charts in Health Care Monitoring and Public Health Surveillance
10.11 Overview of Other Procedures
10.11.1 Tool Wear
10.11.2 Control Charts Based on Other Sample Statistics
10.11.3 Fill Control Problems
10.11.4 Precontrol
10.11.5 Tolerance Interval Control Charts
10.11.6 Monitoring Processes with Censored Data
10.11.7 Monitoring Bernoulli Processes
10.11.8 Nonparametric Control Charts
11 MULTIVARIATE PROCESS MONITORING AND CONTROL
Chapter Overview and Learning Objectives
11.1 The Multivariate Quality-Control Problem
11.2 Description of Multivariate Data
11.2.1 The Multivariate Normal Distribution
11.2.2 The Sample Mean Vector and Covariance Matrix
11.3 The Hotelling T2 Control Chart
11.3.1 Subgrouped Data
11.3.2 Individual Observations
11.4 The Multivariate EWMA Control Chart
11.5 Regression Adjustment
11.6 Control Charts for Monitoring Variability
11.7 Latent Structure Methods
11.7.1 Principal Components
11.7.2 Partial Least Squares
12 ENGINEERING PROCESS CONTROL AND SPC
Chapter Overview and Learning Objectives
12.1 Process Monitoring and Process Regulation
12.2 Process Control by Feedback Adjustment
12.2.1 A Simple Adjustment Scheme: Integral Control
12.2.2 The Adjustment Chart
12.2.3 Variations of the Adjustment Chart
12.2.4 Other Types of Feedback Controllers
12.3 Combining SPC and EPC
PART 5 PROCESS DESIGN AND IMPROVEMENT WITH DESIGNED EXPERIMENTS
13 FACTORIAL AND FRACTIONAL FACTORIAL EXPERIMENTS FOR PROCESS DESIGN AND IMPROVEMENT
Chapter Overview and Learning Objectives
13.1 What is Experimental Design?
13.2 Examples of Designed Experiments In Process and Product Improvement
13.3 Guidelines for Designing Experiments
13.4 Factorial Experiments
13.4.1 An Example
13.4.2 Statistical Analysis
13.4.3 Residual Analysis
13.5 The 2k Factorial Design
13.5.1 The 22 Design
13.5.2 The 2k Design for k ≥ 3 Factors
13.5.3 A Single Replicate of the 2k Design
13.5.4 Addition of Center Points to the 2k Design
13.5.5 Blocking and Confounding in the 2k Design
13.6 Fractional Replication of the 2k Design
13.6.1 The One-Half Fraction of the 2k Design
13.6.2 Smaller Fractions: The 2k−p Fractional Factorial Design
14 PROCESS OPTIMIZATION WITH DESIGNED EXPERIMENTS
Chapter Overview and Learning Objectives
14.1 Response Surface Methods and Designs
14.1.1 The Method of Steepest Ascent
14.1.2 Analysis of a Second-Order Response Surface
14.2 Process Robustness Studies
14.2.1 Background
14.2.2 The Response Surface Approach to Process Robustness Studies
14.3 Evolutionary Operation
PART 6 ACCEPTANCE SAMPLING
15 LOT-BY-LOT ACCEPTANCE SAMPLING FOR ATTRIBUTES
Chapter Overview and Learning Objectives
15.1 The Acceptance-Sampling Problem
15.1.1 Advantages and Disadvantages of Sampling
15.1.2 Types of Sampling Plans
15.1.3 Lot Formation
15.1.4 Random Sampling
15.1.5 Guidelines for Using Acceptance Sampling
15.2 Single-Sampling Plans for Attributes
15.2.1 Definition of a Single-Sampling Plan
15.2.2 The OC Curve
15.2.3 Designing a Single-Sampling Plan with a Specified OC Curve
15.2.4 Rectifying Inspection
15.3 Double, Multiple, and Sequential Sampling
15.3.1 Double-Sampling Plans
15.3.2 Multiple-Sampling Plans
15.3.3 Sequential-Sampling Plans
15.4 Military Standard 105E (ANSI/ASQC Z1.4, ISO 2859)
15.4.1 Description of the Standard
15.4.2 Procedure
15.4.3 Discussion
15.5 The Dodge–Romig Sampling Plans
15.5.1 AOQL Plans
15.5.2 LTPD Plans
15.5.3 Estimation of Process Average
16 OTHER ACCEPTANCE-SAMPLING TECHNIQUES
Chapter Overview and Learning Objectives
16.1 Acceptance Sampling by Variables
16.1.1 Advantages and Disadvantages of Variables Sampling
16.1.2 Types of Sampling Plans Available
16.1.3 Caution in the Use of Variables Sampling
16.2 Designing a Variables Sampling Plan with a Specified OC Curve
16.3 MIL STD 414 (ANSI/ASQC Z1.9)
16.3.1 General Description of the Standard
16.3.2 Use of the Tables
16.3.3 Discussion of MIL STD 414 and ANSI/ASQC Z1.9
16.4 Other Variables Sampling Procedures
16.4.1 Sampling by Variables to Give Assurance Regarding the Lot or Process Mean
16.4.2 Sequential Sampling by Variables
16.5 Chain Sampling
16.6 Continuous Sampling
16.6.1 CSP-1
16.6.2 Other Continuous-Sampling Plans
16.7 Skip-Lot Sampling Plans
APPENDIX
I. Summary of Common Probability Distributions Often Used in Statistical Quality Control
II. Cumulative Standard Normal Distribution
III. Percentage Points of the X2 Distribution
IV. Percentage Points of the t Distribution
V. Percentage Points of the F Distribution
VI. Factors for Constructing Variables Control Charts
VII. Factors for Two-Sided Normal Tolerance Limits
VIII. Factors for One-Sided Normal Tolerance Limits
BIBLIOGRAPHY
ANSWERS TO SELECTED EXERCISES
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