Transcript SPC Montgomery RSM ch14.ppt

Chapter 14
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 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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14.1 Response Surface Methods and Designs
Response surface methodology (RSM) is a collection of techniques for
application where
• A response of interest is influenced by several variables
• The objective is to optimize this response
General approach was developed in early 1950s and applied in the
chemical industry
Has found application in settings such as semiconductor and electronics
manufacturing, machining, metal cutting, and joining processes
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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RSM
• RSM is a sequential procedure
• Factor screening should always come first
• First phase is steepest ascent – moving
efficiently from a poor set of operating
conditions towards the optimum
• Steepest ascent uses the first order model
• When we are near the optimum, a second order
model is used to determine the final estimate
of the optimum operating conditions
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Central Composite Design (CCD)
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The Rotatable CCD
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Robust Parameter Design (RPD) Problem – Taguchi
•
In early 1980s, Taguchi introduce an approach to solving the robust parameter
design (RPD) problem, classifying process variables as
• Control (or controllable) variables and
• Noise (or uncontrollable) variables
•
Made use of highly fractionated factorial designs and other types of fractional
designs obtained from orthogonal arrays, where `an orthogonal design for
controllable factors is “crossed” with a separate orthogonal design for noise factors
(see Table 14.3)
•
Data are summarized for analysis as two statistics
1. The average of each observation in the inner array across all runs in the outer
array, and
2. Signal-to-noise ratios
•
Taguchi design strategy leads to very large experiments (72 runs in Table 14.3)
• However while controllable factor  noise factor interactions can be estimated
(see Figure 14.11), do not provide any information on interactions between
controllable variables
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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In Table 14.3:
Panel (a) contains four controllable factors, each at three levels, and is
referred to as the inner array design
Panel (b) contains three uncontrollable factors, each at two levels, and is
referred to as the outer array design
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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14.3 Evolutionary Operation
• Other process monitoring techniques can be used in situations where a
strong relationship exists between the controllable variable(s) and
observed response variable
• Box (1957) proposed evolutionary operation (EVOP) as an operating
procedure for continuous operation and monitoring of a process
• Goal is to move operating conditions toward the optimum or
following a “drift”
• EVOP consists of systematically introducing small changes in the
levels of the process operating variables
• Changes are assumed to be small enough so that serious
disturbances in product quality will not occur,
• Yet large enough so that potential improvements in process
performance will be eventually discovered
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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The two-level factorial design is the basis of EVOP
Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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Chapter 14
Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2012 John Wiley & Sons, Inc.
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