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