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Chapter 8 2 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 3 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 4 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 5 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 6 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 7 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 8 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 9 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 10 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 11 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Cusum Status Chart (Figure 8-3a)
Chapter 8 12 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
MINITAB calculates the lower cusum this
way
MINITAB Version of Cusum Status Chart
Chapter 8 13 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 14 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Recommendations for Cusum Design
Chapter 8 15 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 16 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Standardized Cusum
Chapter 8 17 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
• Improving cusum performance for large shifts: the combined cusum-Shewhart scheme
Chapter 8 18 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
• Set the starting value equal to H/2
The Fast Initial Response (FIR) Cusum
Chapter 8 19 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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 8 20 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 21 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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 8 22 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 23 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
The Cusum V-Mask
Chapter 8 24 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 25 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 26 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 27 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 28 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Steady-state control limits
Chapter 8 29 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Remaining calculations given in Table 8-9
Chapter 8 30 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Period 1 Control Limits:
Chapter 8 31 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Steady-State Control Limits:
UCL
Chapter 8 32 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 33 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Design of the EWMA
Chapter 8 34 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 35 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Robustness of EWMA toNon-normal Process Data
Chapter 8 36 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 37 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 38 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 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 8 39 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 40 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 41 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
Chapter 8 42 Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery.Copyright (c) 2005 John Wiley & Sons, Inc.
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