Cumulative Sum Charts and Charting for Quality Improvement
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Cumulative Sum Charts and Charting for Quality Improvement

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Description

Covering CUSUMs from an application-oriented viewpoint, while also providing the essential theoretical underpinning, this is an accessible guide for anyone with a basic statistical training. The text is aimed at quality practitioners, teachers and students of quality methodologies, and people interested in analysis of time-ordered data. Further support is available from a Web site containing CUSUM software and data sets.
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Product details

  • Paperback | 247 pages
  • 155 x 235 x 14.22mm | 415g
  • New York, NY, United States
  • English
  • Softcover reprint of the original 1st ed. 1998
  • XVI, 247 p.
  • 1461272459
  • 9781461272458
  • 2,046,417

Table of contents

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.
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About Douglas M. Hawkins

Cumulative Sum Control Charting is a valuable tool for detecting persistent shifts in series of readings. It is used in statistical process control settings such as manufacturing, but it is also effective in areas such as personnel management, econometrics, and data analysis. It is an essential tool for the quality professional.
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