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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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