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Chapter 8 1Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 2Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Learning Objectives
Chapter 8 3Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Process Capability
Natural tolerance limits are defined as follows:
Chapter 8 4
Uses of process capability data:
Chapter 8 5Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Reasons for Poor Process Capability
Process may haveProcess may have good potential
capability
Chapter 8 6Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 7Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 8Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 9Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Probability Plotting
Chapter 8 10Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
• The distribution may not be normal; other types of probability plots can be useful in determining th i t di t ib ti
Chapter 8 11Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
the appropriate distribution.
Chapter 8 12Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 13Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
For the hard bake process:
Chapter 8 14Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
One-Sided PCROne Sided PCR
Chapter 8 15Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Interpretation of the PCR
Chapter 8 16Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Assumptions for Interpretation of Numbers in T bl 8 2Table 8.2
• Violation of these assumptions can lead to big trouble in using the data in Table 8.2.
Chapter 8 17Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 18Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
• Cp does not take process centering into account
• It is a measure of potentialcapability, not actual capability
Chapter 8 19
A Measure of Actual Capability
Chapter 8 20Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Normality and Process Capability Ratiosy p y
• The assumption of normality is critical to the usual p yinterpretation of these ratios (such as Table 8.2)
• For non-normal data, options are1. Transform non-normal data to normal2. Extend the usual definitions of PCRs to handle
l d tnon-normal data3. Modify the definitions of PCRs for general
families of distributionsfamilies of distributions
Chapter 8 21Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Other Types of Process Capability Ratios
• First generationFirst generation• Second generation• Third generation• Third generation • Lots of research has been done to develop ratios that
overcome some of the problems with the basic onesovercome some of the problems with the basic ones• Not much evidence that these ratios are used to any
significant extent in practices g c e e p c ce
Chapter 8 22Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 23Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 24Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 25Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 26Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 27Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 28Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Process CapabilityProcess Capability Analysis using Control Charts
Chapter 8 29Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Since LSL = 200
Chapter 8 30Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 31Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 32Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 33Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 34Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
8.7 Gauge and Measurement Systems8.7 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 measurement system
• Assess whether the gauge is capable (suitable for the intended application)
Chapter 8 35Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 36Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 37Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 38
The P/T (precision-to-tolerance) ratio:
Chapter 8 39Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 40Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Estimating the Variance Components
Chapter 8 41Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 42Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 43Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
The gauge is not capable by this criterion
Discrimination Ratio
Chapter 8 44Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Accuracy and Precision
We have focused only on precision
Chapter 8 45Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Gauge R&R Studies
Chapter 8 46Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Gauge R&R Studies Are Usually Conducted with a Factorial Experimentwith a Factorial Experiment
Chapter 8 47Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
This is a two-factor factorial experiment
ANOVA methods are used to analyze the data and to estimate the variance components
Chapter 8 48Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
estimate the variance components
Chapter 8 49Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 50Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 51Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
• Negative estimates of a variance component would lead to filling a reduced model, such as, f lfor example:
Chapter 8 52Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 53Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
For this Example
Chapter 8 54Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Other Topics in Gauge R&R Studies
• Section 8.7.3 provides a description of methods to p pobtain confidence intervals on the variance components and measures of gauge R&R
• Section 8.7.4 presents a new measure of gauge capability the probabilities of misclassification ofcapability, the probabilities of misclassification of parts– Rejecting good units (producer’s risk)j g g (p )– Passing bad units (consumer’s risk)– Methods for calculating these two probabilities are given
Chapter 8 55Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
8.7.5 Attribute Gauge Capability
• Sometimes the output of a gauge isn’t numerical – it’s just pass/fail
• Nominal or ordinal data is also common• Occurs frequently in service businesses• Common situation – do operating personnel consistently make• Common situation – do operating personnel consistently make
the same decisions regarding the units they are inspecting or analyzingE l b k l d iti f t l• Example – a bank uses manual underwriting of mortgage loans
• The underwriter uses information to classify the applicant into one of four categories; decline or category 1, 2, 3 – categories 2 & 3 are low-risk and 1 is high risk
• Compare underwriters performance relative to a “consensus” evaluation determined by a panel of “experts”
Chapter 8 56Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
y p p
Thirty applicants, three underwritersthree underwriters
Each underwriter evaluates each application twiceapplication twice
The applications are “blinded” by removing names, g ,SSNs, addresses, and other identifying information
Chapter 8 57
Attribute Gauge Capability
• Determine the proportion of time that the underwriter agrees with him/herself – this measures repeatabilityagrees with him/herself this measures repeatability
• Determine the proportion of time that the underwriter agrees with the correct classification – this measures gbias
• Minitab performs the analysis – using the attribute p y gagreement analysis routine
Chapter 8 58Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 59Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 60Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
8.8 Setting Specifications on Discrete CComponents
• Components interact with other componentsComponents interact with other components• Complex assemblies• Tolerance stack-up problems• Tolerance stack-up problems• Linear combinations• Nonlinear combinations• Nonlinear combinations
Chapter 8 61Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 62Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 63Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 64Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 65Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 66Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
8.9 Estimating the Natural Tolerance i i fLimits of a Process
For a normal distribution with unknown mean and variance:
• Difference between tolerance limits and confidence limits
• Nonparametric tolerance limits can also be calculatedNonparametric tolerance limits can also be calculated
Chapter 8 67Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Chapter 8 68Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.
Learning Objectives
Chapter 8 69Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery.Copyright (c) 2009 John Wiley & Sons, Inc.