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Chapter 9 1Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 2Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Learning ObjectivesLearning Objectives

Chapter 9 3Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

9.1 The Cumulative Sum Control Chart

Chapter 9 4

Chapter 9 5Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Cumulative Sum Control Chart

Chapter 9 6Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Tabular Cusum

Chapter 9 7Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 8

Chapter 9 9Introduction 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 10Introduction 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 11Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 12Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Recommendations for Cusum Design

Chapter 9 13Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 14Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Standardized Cusum

Chapter 9 15Introduction 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 16Introduction 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 17Introduction 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 3H = 12 implies that the cusum signals at sample 3

Without the headstart, it would not signal until sample 6

Chapter 9 18Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 19Introduction 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 toshifted off a specified target because it is easy to calculate the required adjustment

One-sided cusums are often usefulO e s ded cusu s e o e use u Cusums can also be used to monitor variability Cusums are available for other sample statisticsCusums are available for other sample statistics

(ranges, standard deviations, counts, proportions) Rational subgroups and cusumsat o a subg oups a d cusu s

Chapter 9 20Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 21Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

The Cusum V-Mask

Chapter 9 22Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 23Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 24Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 25Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 26Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 27Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

9.2 The Exponentially Weighted Moving l hAverage Control Chart

The EWMA is

Chapter 9 28Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 29Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Steady-state control limits

Chapter 9 30Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 31Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 32Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 33Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Design of the EWMA

Chapter 9 34Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 35Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 36Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Robustness of EWMA toNon-normal Process DataNon-normal Process Data

Chapter 9 37Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 38Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 39Introduction 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

M i i i bili Monitoring variability Monitoring count data The EWMA as a predictor of process level

Chapter 9 40Introduction 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 41Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 42Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copight (c) 2009 John Wiley & Sons, Inc.

Chapter 9 43Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Chapter 9 44Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.

Learning Objectives

Chapter 9 45Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.