Transcript SPC Montgomery ch09.ppt

Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Learning Objectives
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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8.1 The Cumulative Sum Control Chart
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Cumulative Sum Control Chart
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Tabular Cusum
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Cusum Status Chart (Figure 9.3a)
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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MINITAB Version of Cusum Status Chart
Minitab calculates the lower Cusum this way
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Recommendations for Cusum Design
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Standardized Cusum
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Improving Cusum Performance for Large Shifts: The
Combined Shewhart-Cusum Scheme
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Fast Initial Response (FIR) Cusum
K = 3, H = 12, headstart = H/2 = 6
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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H = 12 implies that the cusum signals at sample 3
Without the headstart, it would not signal until sample 6
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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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
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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The Cusum V-Mask
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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9.2 The Exponentially Weighted Moving
Average Control Chart
The EWMA is
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Steady-state
control limits
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Design of the EWMA
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Robustness of EWMA to
Non-normal Process Data
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Extensions of the EWMA
•
•
•
•
Fast initial response feature
Monitoring variability
Monitoring count data
The EWMA as a predictor of process level
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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9.3 The Moving Average Control Chart
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Learning Objectives
Chapter 9
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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