6. Process or Product Monitoring and Control 6. Process or Product Monitoring and Control This chapter presents techniques for monitoring and controlling processes and signaling when corrective actions are necessary. 1. Introduction 2. Test Product for Acceptability 1. History 1. Acceptance Sampling 2. Process Control Techniques 2. Kinds of Sampling Plans 3. Process Control 3. Choosing a Single Sampling 4. "Out of Control" Plan 5. "In Control" but Unacceptable 4. Double Sampling Plans 6. Process Capability 5. Multiple Sampling Plans 6. Sequential Sampling Plans 7. Skip Lot Sampling Plans 3. Univariate and Multivariate 4. Time Series Models Control Charts 1. Definitions, Applications and 1. Control Charts Techniques 2. Variables Control Charts 2. Moving Average or 3. Attributes Control Charts Smoothing Techniques 4. Multivariate Control charts 3. Exponential Smoothing 4. Univariate Time Series Models 5. Multivariate Time Series Models 5. Tutorials 6. Case Study 1. What do we mean by 1. Lithography Process Data "Normal" data? 2. Box-Jenkins Modeling 2. What to do when data are non- Example normal 3. Elements of Matrix Algebra 4. Elements of Multivariate Analysis 5. Principal Components Detailed Table of Contents References http://www.itl.nist.gov/div898/handbook/pmc/pmc.htm[6/27/2012 2:37:20 PM] 6. Process or Product Monitoring and Control 6. Process or Product Monitoring and Control - Detailed Table of Contents [6.] 1. Introduction [6.1.] 1. How did Statistical Quality Control Begin? [6.1.1.] 2. What are Process Control Techniques? [6.1.2.] 3. What is Process Control? [6.1.3.] 4. What to do if the process is "Out of Control"? [6.1.4.] 5. What to do if "In Control" but Unacceptable? [6.1.5.] 6. What is Process Capability? [6.1.6.] 2. Test Product for Acceptability: Lot Acceptance Sampling [6.2.] 1. What is Acceptance Sampling? [6.2.1.] 2. What kinds of Lot Acceptance Sampling Plans (LASPs) are there? [6.2.2.] 3. How do you Choose a Single Sampling Plan? [6.2.3.] 1. Choosing a Sampling Plan: MIL Standard 105D [6.2.3.1.] 2. Choosing a Sampling Plan with a given OC Curve [6.2.3.2.] 4. What is Double Sampling? [6.2.4.] 5. What is Multiple Sampling? [6.2.5.] 6. What is a Sequential Sampling Plan? [6.2.6.] 7. What is Skip Lot Sampling? [6.2.7.] 3. Univariate and Multivariate Control Charts [6.3.] 1. What are Control Charts? [6.3.1.] 2. What are Variables Control Charts? [6.3.2.] 1. Shewhart X-bar and R and S Control Charts [6.3.2.1.] 2. Individuals Control Charts [6.3.2.2.] 3. Cusum Control Charts [6.3.2.3.] 1. Cusum Average Run Length [6.3.2.3.1.] 4. EWMA Control Charts [6.3.2.4.] 3. What are Attributes Control Charts? [6.3.3.] 1. Counts Control Charts [6.3.3.1.] 2. Proportions Control Charts [6.3.3.2.] 4. What are Multivariate Control Charts? [6.3.4.] 1. Hotelling Control Charts [6.3.4.1.] 2. Principal Components Control Charts [6.3.4.2.] 3. Multivariate EWMA Charts [6.3.4.3.] 4. Introduction to Time Series Analysis [6.4.] 1. Definitions, Applications and Techniques [6.4.1.] 2. What are Moving Average or Smoothing Techniques? [6.4.2.] 1. Single Moving Average [6.4.2.1.] 2. Centered Moving Average [6.4.2.2.] http://www.itl.nist.gov/div898/handbook/pmc/pmc_d.htm[6/27/2012 2:35:29 PM] 6. Process or Product Monitoring and Control 3. What is Exponential Smoothing? [6.4.3.] 1. Single Exponential Smoothing [6.4.3.1.] 2. Forecasting with Single Exponential Smoothing [6.4.3.2.] 3. Double Exponential Smoothing [6.4.3.3.] 4. Forecasting with Double Exponential Smoothing(LASP) [6.4.3.4.] 5. Triple Exponential Smoothing [6.4.3.5.] 6. Example of Triple Exponential Smoothing [6.4.3.6.] 7. Exponential Smoothing Summary [6.4.3.7.] 4. Univariate Time Series Models [6.4.4.] 1. Sample Data Sets [6.4.4.1.] 1. Data Set of Monthly CO2 Concentrations [6.4.4.1.1.] 2. Data Set of Southern Oscillations [6.4.4.1.2.] 2. Stationarity [6.4.4.2.] 3. Seasonality [6.4.4.3.] 1. Seasonal Subseries Plot [6.4.4.3.1.] 4. Common Approaches to Univariate Time Series [6.4.4.4.] 5. Box-Jenkins Models [6.4.4.5.] 6. Box-Jenkins Model Identification [6.4.4.6.] 1. Model Identification for Southern Oscillations Data [6.4.4.6.1.] 2. Model Identification for the CO2 Concentrations Data [6.4.4.6.2.] 3. Partial Autocorrelation Plot [6.4.4.6.3.] 7. Box-Jenkins Model Estimation [6.4.4.7.] 8. Box-Jenkins Model Diagnostics [6.4.4.8.] 1. Box-Ljung Test [6.4.4.8.1.] 9. Example of Univariate Box-Jenkins Analysis [6.4.4.9.] 10. Box-Jenkins Analysis on Seasonal Data [6.4.4.10.] 5. Multivariate Time Series Models [6.4.5.] 1. Example of Multivariate Time Series Analysis [6.4.5.1.] 5. Tutorials [6.5.] 1. What do we mean by "Normal" data? [6.5.1.] 2. What do we do when data are "Non-normal"? [6.5.2.] 3. Elements of Matrix Algebra [6.5.3.] 1. Numerical Examples [6.5.3.1.] 2. Determinant and Eigenstructure [6.5.3.2.] 4. Elements of Multivariate Analysis [6.5.4.] 1. Mean Vector and Covariance Matrix [6.5.4.1.] 2. The Multivariate Normal Distribution [6.5.4.2.] 3. Hotelling's T squared [6.5.4.3.] 1. T2 Chart for Subgroup Averages -- Phase I [6.5.4.3.1.] 2. T2 Chart for Subgroup Averages -- Phase II [6.5.4.3.2.] 3. Chart for Individual Observations -- Phase I [6.5.4.3.3.] 4. Chart for Individual Observations -- Phase II [6.5.4.3.4.] 5. Charts for Controlling Multivariate Variability [6.5.4.3.5.] 6. Constructing Multivariate Charts [6.5.4.3.6.] 5. Principal Components [6.5.5.] 1. Properties of Principal Components [6.5.5.1.] 2. Numerical Example [6.5.5.2.] 6. Case Studies in Process Monitoring [6.6.] 1. Lithography Process [6.6.1.] 1. Background and Data [6.6.1.1.] 2. Graphical Representation of the Data [6.6.1.2.] http://www.itl.nist.gov/div898/handbook/pmc/pmc_d.htm[6/27/2012 2:35:29 PM] 6. Process or Product Monitoring and Control 3. Subgroup Analysis [6.6.1.3.] 4. Shewhart Control Chart [6.6.1.4.] 5. Work This Example Yourself [6.6.1.5.] 2. Aerosol Particle Size [6.6.2.] 1. Background and Data [6.6.2.1.] 2. Model Identification [6.6.2.2.] 3. Model Estimation [6.6.2.3.] 4. Model Validation [6.6.2.4.] 5. Work This Example Yourself [6.6.2.5.] 7. References [6.7.] http://www.itl.nist.gov/div898/handbook/pmc/pmc_d.htm[6/27/2012 2:35:29 PM] 6.1. Introduction 6. Process or Product Monitoring and Control 6.1. Introduction Contents This section discusses the basic concepts of statistical process of Section control, quality control and process capability. 1. How did Statistical Quality Control Begin? 2. What are Process Control Techniques? 3. What is Process Control? 4. What to do if the process is "Out of Control"? 5. What to do if "In Control" but Unacceptable? 6. What is Process Capability? http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc1.htm[6/27/2012 2:35:35 PM] 6.1.1. How did Statistical Quality Control Begin? 6. Process or Product Monitoring and Control 6.1. Introduction 6.1.1. How did Statistical Quality Control Begin? Historical Quality Control has been with us for a long time. How perspective long? It is safe to say that when manufacturing began and competition accompanied manufacturing, consumers would compare and choose the most attractive product (barring a monopoly of course). If manufacturer A discovered that manufacturer B's profits soared, the former tried to improve his/her offerings, probably by improving the quality of the output, and/or lowering the price. Improvement of quality did not necessarily stop with the product - but also included the process used for making the product. The process was held in high esteem, as manifested by the medieval guilds of the Middle Ages. These guilds mandated long periods of training for apprentices, and those who were aiming to become master craftsmen had to demonstrate evidence of their ability. Such procedures were, in general, aimed at the maintenance and improvement of the quality of the process. In modern times we have professional societies, governmental regulatory bodies such as the Food and Drug Administration, factory inspection, etc., aimed at assuring the quality of products sold to consumers. Quality Control has thus had a long history. Science of On the other hand, statistical quality control is statistics is comparatively new. The science of statistics itself goes fairly recent back only two to three centuries. And its greatest developments have taken place during the 20th century. The earlier applications were made in astronomy and physics and in the biological and social sciences. It was not until the 1920s that statistical theory began to be applied effectively to quality control as a result of the development of sampling theory. The concept of The first to apply the newly discovered statistical methods quality to the problem of quality control was Walter A. Shewhart control in of the Bell Telephone Laboratories. He issued a manufacturing memorandum on May 16, 1924 that featured a sketch of a was first modern control chart.