Algorithmic statistical process control: concepts and an application
TL;DR: This methodology seeks to exploit the strengths of both automatic control and statistical process control, two fields that have developed in relative isolation from one another.
Abstract: The goal of algorithmic statistical process control is to reduce predictable quality variations using feedback and feedforward techniques and then monitor the complete system to detect and remove unexpected root causes of variation. This methodology seeks to exploit the strengths of both automatic control and statistical process control (SPC), two fields that have developed in relative isolation from one another. Recent experience with the control and monitoring of intrinsic viscosity from a particular General Electric polymerization process has led to a better understanding of how SPC and feedback control can be united into a single system. Building on past work by MacGregor, Box, Astrom, and others, the article covers the application from statistical identification and modeling to implementing feedback control and final SPC monitoring. Operational and technical issues that arose are examined, and a general approach is outlined.
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2,730 citations
TL;DR: The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered and multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches.
Abstract: The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.
1,359 citations
TL;DR: Multivariate statistical procedures for monitoring the progress of batch processes are developed using multi-way partial least squares for extracting information from the process measurement variable trajectories that is more relevant to the final quality variables of the product.
703 citations
Book•
23 Jan 1998
TL;DR: In this article, the authors present a CUSUM chart for a normal mean and compare it to the Shewhart Xbar chart for the same purpose, showing the effect of the change in the normal distribution.
Abstract: 1 Introduction.- 1.1 Common-cause and special-cause variability.- 1.2 Transient and persistent special causes.- 1.3 The Shewhart and CUSUM charts.- 1.4 Basis for the CUSUM chart for a normal mean.- 1.4.1 Statistical properties of the CUSUM.- 1.5 Out-of-control distribution of the CUSUM.- 1.6 Testing for a shift -the V mask.- 1.7 Estimation following a signal.- 1.8 Using individual readings or rational groups.- 1.9 The decision interval form of the CUSUM.- 1.9.1 Example.- 1.10 Summary.- 1.11 Further reading.- 2 CUSUM design.- 2.1 The choice of k and h.- 2.1.1 Reference value k - "tuning" for a specific shift.- 2.2 Runs, run length, and average run length.- 2.2.1 The choice of h, the decision interval.- 2.2.2 Calculating the k, h, ARL relationship.- 2.2.3 A closer look at the choice of in-control ARL.- 2.2.4 Designing a CUSUM of Xbar.- 2.3 The Shewhart Xbar chart as CUSUM.- 2.4 Summary.- 2.5 Further reading.- 3 More about normal data.- 3.1 In-control ARLs.- 3.2 Out-of-control ARLs.- 3.2.1 Model.- 3.2.2 The ARL following a shift in mean.- 3.3.3 ARL sensitivity to choice of K.- 3.2.4 Out-of-control states and two-sided CUSUMs.- 3.3 FIR CUSUMs: zero start and steady state start.- 3.3.1 Introduction.- 3.3.2 Out-of-control ARL of the FIR CUSUM.- 3.3.3 ARL of two-sided FIR CUSUMS.- 3.3.4 Initial and steady-state ARL.- 3.4 Controlling for the mean within a range.- 3.4.1 Example.- 3.5 The impact of variance shifts.- 3.5.1 Individual data -the approximate normal transform.- 3.5.2 Rational groups-variance CUSUMs.- 3.6 Combined Shewhart and CUSUM charts.- 3.6.1 Example.- 3.7 Effect of model departures.- 3.7.1 Nonnormality.- 3.7.2 Independence.- 3.8 Weighted CUSUMs.- 3.8.1 Example.- 3.9 Summary.- 3.10 Further reading.- 4 Other continuous distributions.- 4.1 The gamma family and normal variances.- 4.1.1 Background.- 4.1.2 Normal variances.- 4.1.3 Design of the CUSUM for scale.- 4.1.4 Example: Sugar bags.- 4.1.5 Shift in the gamma shape parameter ?.- 4.1.6 Example - shift in ss.- 4.2 The inverse Gaussian family.- 4.2.1 Background.- 4.2.2 Shift in mean.- 4.2.3 Shift in scale parameter.- 4.3 Example from General Motors.- 4.3.1 CUSUM chart for location.- 4.3.2 CUSUM chart for ?.- 4.3.3 Remarks.- 4.4 Comments.- 4.5 Further reading.- 5 Discrete data.- 5.1 Types of discrete data.- 5.1.1 Binomial data.- 5.1.2 Count data.- 5.2 The graininess of the ARL function.- 5.3 The Poisson distribution and count data.- 5.3.1 Useful properties of the Poisson distribution.- 5.4 The Poisson and CUSUMs.- 5.4.1 Design for an upward shift.- 5.4.2 Downward shift.- 5.4.3 ARLs.- 5.4.4 Example.- 5.4.5 The effect of departures from Poisson.- 5.4.6 Checking conformity to the Poisson model.- 5.5 Weighted Poisson CUSUMs.- 5.6 The binomial distribution.- 5.6.1 Background.- 5.6.2 Examples.- 5.6.3 The choice of m.- 5.7 Weighted binomial CUSUMs.- 5.7.1 Example.- 5.8 Other discrete distributions.- 5.9 Summary.- 5.10 Further reading.- 6 Theoretical foundations of the CUSUM.- 6.1 General theory.- 6.1.1 Relation of the SPRT to the CUSUM.- 6.1.2 Optimality properties.- 6.2 The general exponential family.- 6.2.1 Derivation of the CUSUM for a normal mean shift.- 6.2.2 The gamma family and normal variance.- 6.2.3 Relation to normal variances.- 6.2.4 The Poisson family.- 6.2.5 The binomial family.- 6.2.6 The negative binomial family.- 6.2.7 The inverse Gaussian family.- 6.2.8 The Weibull distribution.- 6.2.9 Distributions outside the exponential family.- 6.3 The Markov property of CUSUMs.- 6.4 Getting the ARL.- 6.4.1 The renewal equations.- 6.4.2 The Markov chain approach.- 6.4.3 Simulation using variance reduction techniques.- 6.5 Summary.- 6.6 Further reading.- 7 Calibration and short runs.- 7.1 The self-starting approach.- 7.2 The self-starting CUSUM for a normal mean.- 7.2.1 Special features of self-starting charts.- 7.3 Self-starting CUSUMs for gamma data.- 7.3.1 Background.- 7.3.2 The scheme.- 7.3.3 Example.- 7.3.4 Normal data - control of mean and variance.- 7.3.5 Comments.- 7.4 Discrete data.- 7.4.1 The Poisson distribution.- 7.4.2 The binomial distribution.- 7.4.3 Updating the targets.- 7.5 Summary.- 7.6 Further reading.- 8 Multivariate data.- 8.1 Outline of the multivariate normal.- 8.2 Shewhart charting-Hotelling's T2.- 8.3 CUSUM charting - various approaches.- 8.3.1 Collections of unvariate CUSUMs.- 8.4 Regression adjustment.- 8.4.1 Example.- 8.4.2 SPC use of regression-adjusted variables.- 8.4.3 Example - monitoring a carbide plant.- 8.5 Choice of regression adjustment.- 8.6 The use of several regression-adjusted variables.- 8.6.1 Example.- 8.7 The multivariate exponentially weighted moving average.- 8.8 Summary.- 8.9 Further reading.- 9 Special topics.- 9.1 Robust CUSUMs.- 9.2 Recursive residuals in regression.- 9.2.1 Definition and properties.- 9.2.2 Example.- 9.3 Autocorrelated data.- 9.3.1 Example.- 9.4 Summary.- 9.5 Further reading.- 9.5.1 Time series.- 9.5.2 Score methods.- 9.5.3 Robustification.- 9.5.4 Recursive residuals.- 10 Software.- 10.1 Programs and templates.- 10.2 Data files.- References.
653 citations
TL;DR: An overview of current research on control charting methods for process monitoring and improvement and a historical perspective and ideas for future research are given.
Abstract: An overview is given of current research on control charting methods for process monitoring and improvement. A historical perspective and ideas for future research also are given. Research topics include: variable sample size and sampling interval met..
647 citations
References
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Book•
01 Jan 1970
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Abstract: From the Publisher:
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.
19,748 citations
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.
Abstract: From the Publisher:
This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.
12,650 citations
"Algorithmic statistical process con..." refers background or methods in this paper
...The standard textbooks by Astrom (1970) and Box and Jenkins (1970, 1976) gave solutions to the minimum MSE feedback problem for general ARMAX systems....
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...Classic references are Astrom (1970) and Box and Jenkins (1970, 1976)....
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Book•
01 Jun 1976
TL;DR: In this paper, Fourier analysis is used to estimate the mean and autocorrelations of the Fourier spectral properties of a Fourier wavelet and the estimated spectrum of the wavelet.
Abstract: Moving Average and Autoregressive Processes. Introduction to Fourier Analysis. Spectral Theory and Filtering. Some Large Sample Theory. Estimation of the Mean and Autocorrelations. The Periodogram, Estimated Spectrum. Parameter Estimation. Regression, Trend, and Seasonality. Unit Root and Explosive Time Series. Bibliography. Index.
4,532 citations
2,730 citations
"Algorithmic statistical process con..." refers background in this paper
...A quite separate body of literature is that of SPC. Early developments in quality monitoring are due to Shewhart (1931), and an often cited textbook is that of Duncan (1986)....
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