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Chapter 9 1Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 2Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
8.1 The Cumulative Sum Control Chart
Chapter 9 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 4Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The Cumulative Sum Control Chart
Chapter 9 5Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The Tabular Cusum
Chapter 9 6Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 7Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 8Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 9Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Cusum Status Chart (Figure 9.3a)
Chapter 9 10Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
MINITAB Version of Cusum Status Chart
Minitab calculates the lower Cusum this way
Chapter 9 11Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 12Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Recommendations for Cusum Design
Chapter 9 13Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 14Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The Standardized Cusum
Chapter 9 15Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Improving Cusum Performance for Large Shifts: The
Combined Shewhart-Cusum Scheme
Chapter 9 16Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The Fast Initial Response (FIR) Cusum
K = 3, H = 12, headstart = H/2 = 6
Chapter 9 17Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
H = 12 implies that the cusum signals at sample 3
Without the headstart, it would not signal until sample 6
Chapter 9 18Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 19Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
More on Cusums
• Cusums are often used to determine if a process has
shifted off a specified target because it is easy to
calculate the required adjustment
• One-sided cusums are often useful
• Cusums can also be used to monitor variability
• Cusums are available for other sample statistics
(ranges, standard deviations, counts, proportions)
• Rational subgroups and cusums
Chapter 9 20Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 21Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The Cusum V-Mask
Chapter 9 22Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 23Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 24Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 25Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 26Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 27Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
9.2 The Exponentially Weighted Moving
Average Control Chart
The EWMA is
Chapter 9 28Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 29Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Steady-state
control limits
Chapter 9 30Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 31Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 32Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 33Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Design of the EWMA
Chapter 9 34Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 35Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 36Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Robustness of EWMA to
Non-normal Process Data
Chapter 9 37Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 38Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 39Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Extensions of the EWMA
• Fast initial response feature
• Monitoring variability
• Monitoring count data
• The EWMA as a predictor of process level
Chapter 9 40Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
9.3 The Moving Average Control Chart
Chapter 9 41Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 9 42Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
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