STATISTICAL QUALITY CONTROL

Transcription

1 Applied Mathematics Volume 10 STATISTICAL QUALITY CONTROL A Loss Minimization Approach Dan Trietsch MSIS Department University ofauckland New Zealand fij World Scientific Sinaapore*NewJerseyLondon» Singapore»New Jersey London Hong Kong

2 Table of Contents Preface vii Chapter 1. Introduction to Shewhart Control Charts What is "Statistical Control" and What is it Good for? Types of Control Charts The Role of Control Charts in Improvement Projects "Fix the Process, Not the Blame!" The Two-Steps Process Improvement Procedure Establishing Control Limits Ways and Means to Abuse Control Charts 14 Chapter 2. On Measurement Measurements That Are Relevant Defining Measurements Operationally Accuracy and Precision Measuring the Quality of Measurements A Possible Remedy for Imprecise Measurements The Danger of Using Highly Biased Measurements Cost-Effectiveness in Measurement Conclusion 33 Supplement 2. More on Precision and Calibration Analyzing the Rules of Thumb for C p =l 35 S The Implications of the Borderline Case for Other Cases Application-Dependent Measurement Errors Deriving the Shewhart/Tippett Formula 43 XI

3 Xll Statistical Quality Control Chapter 3. Partial Measurement of Quality by Loss Functions and Production Costs Loss Functions Calculating the Expected Quadratic Loss (EQL) Loss Functions for "smaller-is-better" and "larger-is-better" Process Capability Indices Production Costs as Part of Measuring Quality Taguchi's Method to Estimate the QLF and Set Optimal Tolerance Limits A Special Case: Processes that are Not Capable Selecting a Process The Lack of Validity of Signal-to-Noise Ratios Variance Reduction and the Pareto Principle 65 Supplement 3. Asymmetrical Loss Functions 69 Chapter 4. Adjusting Processes Without Tampering 4.1. Ways and Means to Tamper The Nelson Funnel Rules Discriminating and Correcting Based on Common Variation Regression to the Mean 4.2. Efficient Adjustment Methods Adjusting an In-Control Process and Tampering are NOT Equivalent The Harmonie Adjustment Rule Numerical example The Robustness of the Harmonie Rule Imprecise adjustment Inaecurate adjustment A comparison with fractional adjustment The Generalized Harmonie Rule Numerical example The Five/Ten Rule

4 Table of Contents Xlll Adjusting Processes with Highly Asymmetrical Loss Functions Setting Economical Tolerances for Processes with Drift Setting Optimal Adjustment Tolerances The Impact of Drift on Product Tolerance Setting HowtoAdjust 112 Chapter 5. Shewhart Control Charts for Attributes np Control Charts for a Single Attribute Recalculating the Control Limits An Example: Deming's Red Beads Experiment Mixtures p Control Charts for a Single Attribute with Varying Subgroup Size Mixtures c Control Charts for the Number of Occurrences in a Constant Area of Opportunity Dement Control Charts The COPQ Chart - A Special Case ofthe Demerit Control Chart Critique of Demerit and of COPQ Control Charts u Control Charts for the Number of Occurrences in a Variable Area of Opportunity Demerit Control Charts with Unequal Areas of Opportunity Common Errors to Avoid 152 Supplement 5. The Relationship Between Control Charts and Hypothesis Testing 153 Chapter 6. Control Charts for Continuous Variables Principles Common to All Shewhart Variable Control Charts Drawing the Centerline for the x Chart Monitoring Quadratic Loss Directly An Option The Normality Assumption 166

5 XIV Statistical Quality Control 6.2. x and s Control Charts and s 2 Charts and R Control Charts Control Charts for Individual Data On the Power of Control Charts CUSUM and EWMA Control Charts CUSUM Charts EWMA Charts Pattern Tests and the Power to Detect Small Shifis Median and Range Control Charts Common Errors to Avoid 223 Supplement 6.1. On the Efficiency of Various Dispersion Statistics The Efficiency of R as a Function of n The Efficiency of Ä Relative to The Efficiency of 7 Relative to s Supplement 6.2. On the Computation of Control Chart Factors Deriving c Deriving ä\ and d Supplement 6.3. More on the Optimal Subgroup Size in Shewhart Control Charts An Approximate Optimization of Subgroup Size to Detect a Shift of Da x Using the Approximation with EWMA Charts Charts with Power to Detect Both Small and Large Deviations 242 Chapter 7. Pattern Tests for Shewhart Control Charts 7.1. Tests for Assignable Causes Applying the Tests to Attribute Charts An example 7.2. Computing the Rate of False Signals (RFS) 7.3. Mixtures, Cycles, Trends, and Erratic Points 7.4. Applying the Tests to Single Charts

6 Table of Contents xv 7.5. Run-Count Tests The Number of Runs Associated with Tests 2 and 4a The Number of Runs Associated with Tests 3 and The Robustness of the Count Method Common Errors to Avoid 267 Supplement 7. Basic Concepts in Time Series Analysis Non-Random Causes of Process Variation Statistically Dependent Causes The Four Basic Processes and Associated Forecasting Methods The Constant Expectation Process A Basic Time-Dependent Process Martingales Sub-Martingales Interim Conclusion Basic Processes and the Nelson Funnel Rules More Sophisticated Analyses 279 Chapter 8. Diffidence Analysis of Control Charts and Diffidence Charts Sources of Diffidence The Diffidence of Attribute Charts Diffidence Charts for Attributes The Diffidence of Continuous Variable Charts The Variation Associated with Estimating afrom Data RFS Variation in s Charts RFS Variation in ~x Charts Combining the results for both Charts Diffidence Charts for Continuous Variables Dynamic Control Limits Diffidence Charts for Dispersion Diffidence Charts for Diffidence and Pattern Tests Diffidence and Inaction are NOT Identical 306 Chapter 9. Inspection Theory 309

7 XVI Statistical Quality Control 9.1. Sampling Versus Deming's kp Rule The Connection Between Inspection and Management By Constraints (MBC) General Inspection Issues On the Mechanics of Random Sampling Who Should Perform Inspections? On the Reliabiüty of Human Inspection Systems More on the kp Rule When Sampling is Not Futile Deming's Recommendations for Cases that Justify Sampling A Heuristic Approach to Reduce the Cost of Inspection and Production The "First and Last" Inspection Rule Devising Single Sampling («, c) Plans Why the Customer Should Not Dictate AQL and a Why LTPD Must Exceed AQL Operating Characteristics Curves for (n, c) Plans Finding (n, c) Plans Methodically Sequential Sampling Plans Constructing Sequential Sampling Plans On Curtailment Average Outgoing Quality Limit (AOQL) 350 References 353 Index 363