Chapter 9 1 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc.
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Chapter 9 1 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 2 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 3 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Learning Objectives
Chapter 9 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
8.1 The Cumulative Sum Control Chart
Chapter 9 5 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 6 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
The Cumulative Sum Control Chart
Chapter 9 7 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
The Tabular Cusum
Chapter 9 8 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 9 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 10 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Cusum Status Chart (Figure 9.3a)
Chapter 9 11 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
MINITAB Version of Cusum Status Chart
Minitab calculates the lower Cusum this way
Chapter 9 12 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 13 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Recommendations for Cusum Design
Chapter 9 14 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 15 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
The Standardized Cusum
Chapter 9 16 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Improving Cusum Performance for Large Shifts: The
Combined Shewhart-Cusum Scheme
Chapter 9 17 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
The Fast Initial Response (FIR) Cusum
K = 3, H = 12, headstart = H/2 = 6
Chapter 9 18 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 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 19 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 20 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 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 21 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 22 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
The Cusum V-Mask
Chapter 9 23 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 24 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 25 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 26 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 27 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 28 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
9.2 The Exponentially Weighted Moving
Average Control Chart
The EWMA is
Chapter 9 29 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 30 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Steady-state
control limits
Chapter 9 31 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 32 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 33 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 34 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Design of the EWMA
Chapter 9 35 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 36 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 37 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Robustness of EWMA to
Non-normal Process Data
Chapter 9 38 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 39 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 40 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 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 41 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
9.3 The Moving Average Control Chart
Chapter 9 42 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 43 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 44 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 9 45 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.
Copyright (c) 2009 John Wiley & Sons, Inc.
Learning Objectives