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Chapter 8 1Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Learning Objectives
Chapter 8 2Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Process Capability
Natural tolerance limits are defined as follows:
Chapter 8 3Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Uses of process capability data:
Chapter 8 4Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Reasons for Poor Process Capability
Chapter 8 5Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Process may have
good potential
capability
Chapter 8 6Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 7Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 8Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Probability Plotting
Chapter 8 9Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 8 10Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
• The distribution may not be normal; other types of
probability plots can be useful in determining the
appropriate distribution.
Chapter 8 11Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 12Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
This is the percentage of the specification band used up by the process.
Chapter 8 13Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
For the hard bake process:
One-Sided PCR
Chapter 8 14Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Interpretation of the PCR
Chapter 8 15Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Assumptions for Interpretation of
Numbers in Table 8.2
Chapter 8 16Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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• Violation of these assumptions can lead to big trouble in using the
data in Table 8.2.
Chapter 8 17Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
• Cp does not take
process centering
into account
• It is a measure
of potential
capability, not
actual capability
Chapter 8 18Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
actual capability
A Measure of Actual Capability
Chapter 8 19Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Normality and Process Capability
Ratios
• The assumption of normality is critical to the usual interpretation of these ratios (such as Table 8.2)
• For non-normal data, options are
Chapter 8 20Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
• For non-normal data, options are
1. Transform non-normal data to normal
2. Extend the usual definitions of PCRs to handle non-normal data
3. Modify the definitions of PCRs for general families of distributions
Chapter 8 21Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 22Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 23Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 24Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Process Capability
Analysis using Control
Charts
Chapter 8 25Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Since LSL = 200
Chapter 8 26Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Since LSL = 200
7.8 Gauge and Measurement Systems
Capability Studies
• Determine how much of the observed
variability is due to the gauge or measurement
system
• Isolate the components of variability in the
Chapter 8 27Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
• Isolate the components of variability in the
measurement system
• Assess whether the gauge is capable (suitable
for the intended application)
Chapter 8 28Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 29Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 30Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The P/T ratio:
Chapter 8 31Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 32Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Estimating the Variance Components
Chapter 8 33Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
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Chapter 8 34Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 35Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
The gauge is not capable by this criterion
Discrimination Ratio
Chapter 8 36Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Accuracy and Precision
We have
focused only on
precision
Chapter 8 37Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
precision
Gauge R&R Studies
Chapter 8 38Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Gauge R&R Studies Are Usually Conducted
with a Factorial Experiment
Chapter 8 39Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 40Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
This is a two-factor factorial experiment
ANOVA methods are used to analyze the data and yo estimate the
variance components
Chapter 8 41Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 42Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 43Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 44Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
• Negative estimates of a variance component
would lead to filling a reduced model, such as,
for example:
Chapter 8 45Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 46Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
For this Example
Chapter 8 47Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
Chapter 8 48Statistical Quality Control, 7th Edition by Douglas C. Montgomery.
Copyright (c) 2013 John Wiley & Sons, Inc.
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