Desk Reference of Statistical Quality Methods

541 Pages·2008·4.314 MB·English

by  Crossley, Mark L.

The Desk Reference
of Statistical
Quality Methods
Second Edition
Mark L. Crossley
ASQ Quality Press
Milwaukee, Wisconsin
American Society for Quality, Quality Press, Milwaukee 53203
©2008 by American Society for Quality
All rights reserved. Published 2007
Printed in the United States of America
13 12 11 10 09 08 07 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Crossley, Mark L.
The desk reference of statistical quality methods / Mark L. Crossley.
p. cm.
ISBN 978-0-87389-725-9 (alk. paper)
1. Quality control—Statistical methods. 2. Process control—Statistical
methods. I. Title.
TS156.C79 2007
658.5′62—dc22 2007033871
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recording, or otherwise, without the prior written permission of the publisher.
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Preface
This desk reference provides the quality practitioner with a single resource that illustrates
in a practical manner exactly how to execute specific statistical methods frequently used
in the quality sciences. This reference is not intended to be a rigorously theoretical treatise
on the subject; rather, it briefly describes how to use a tool or technique. Aplethora of top-
ics have been arranged in alphabetical order, ranging from Accelerated Reliability Testing
to Zone Format Control Chart.At the end of most topics is a bibliography. All of the exam-
ples in this reference are based on data that are purely hypothetical and fictitious in nature.
This desk reference does not assume that the reader has already been exposed to the details
of a specific topic but perhaps has some familiarity with the topic and wants more infor-
mation regarding its application. This reference is accessible for the average quality prac-
titioner, who will need a minimal prior understanding of the techniques discussed to ben-
efit from them. Each topic is presented in a stand-alone fashion with, in most cases, several
examples detailing computational steps and application comments.
How to Use This Reference
There are 48 individual modules, or topics, in this desk reference (see Usage Matrix
Table). These modules fall into one of the following seven major categories that are
defined as a function of the topic’s application.
Descriptive Methods
These tools and techniques are used to measure selected parameters such as the central ten-
dency, variation, probabilities, data presentation methods, and other single-value responses
such as measurement error and process capability indices. Topics in this category answer
such questions as: What size sample should I take to determine the average of a process?
How much error do I have using my current measurement system? How large of a sample
do I take to be 90 percent confident that the true C is not less than 1.20? If the measured
pk
kurtosis of my data distribution is +0.75, is the distribution considered normal? What is the
hypergeometric distribution, and when do I use it? Will my error for the proportion be
affected if my sample size represents a significant proportion of my population?
xiii
xiv Preface
Statistical Process Control (Basic)
Traditional methods of statistical process control (SPC) and its general use are presented.
SPC assists in the determination of process changes. Topics in this category answer such
questions as: What is the probability that I will detect a process shift of +0.53 using an
average/range control chart with n = 5 within seven samples after the shift has occurred?
Why is the average/range control chart more robust with respect to a nonnormally distrib-
uted population than the individual/moving range control chart?
SPC (Special Applications)
Traditional methods of SPC are extended to include short-run applications, detection of
changes in distributions, and non-Shewhart methods. Topics in this section answer such
questions as: What control chart do I use if I only want to detect a change in the distribu-
tion of the data? How do I use a pchart when my defect rate is extremely low? What con-
trol chart can I use to make the charting process user friendly? Is there a control chart
based on specification limits?
Process Improvement
Certain techniques can be used to improve processes by reducing variation or optimizing
operating conditions. These techniques provide the means to improve processes by
addressing such questions as: Can I use design of experiments on a continuous basis for
process improvement? How do I use design of experiment to reduce variation?
Reliability
This section provides analysis of life data and applications related to the understanding of
product reliability. These topics address such issues as: I have calculated the MTBF from
12 failure times; how do I determine the 90 percent confidence interval? What is the bath-
tub curve, and how does failure rate relate to the age of a product? How can I graphically
estimate the parameters of the Weibull distribution?
Comparative Data Analysis
Comparative data analysis includes methods to compare observed data with expected val-
ues and with compare sets of data with each other. These methods are frequently used to
determine whether differences in populations exist. Typical questions answered using
these techniques are: I have determined that my process average is 12.0 using 25 samples;
have I achieved my goal of 11.5 minimum based on these sample data? The old process
was running at 7.6 percent defective (based on a sample of n = 450), and the new and
improved process is 5.6 percent defective (based on 155 samples); have I actually
improved the process?
Preface xv
Acceptance Sampling Plans
Acceptance sampling plans are schemes used to assist in the decision to accept or reject
lots of materials based on sampling data for either variables or attributes. This section
addresses such concerns as: Can I develop my own sampling plans, or must I depend on
published plans? What affects the operating characteristic more—the sample size or the lot
size?
The following list organizes the modules according to the aforementioned categories:
Descriptive Methods
Confidence Interval for the Average
Confidence Interval for the Proportion
Confidence Interval for the Standard Deviation
Descriptive Statistics
Discrete Distributions
Histograms
Measurement Error Assessment
Nonnormal Distribution C
pk
Normal Distribution
Pareto Analysis
Pre-Control
Process Capability Indices
Regression and Correlation
SPC (Basic)
Average/Range Control Chart
Average/Standard Deviation Control Chart
Chart Resolution
Defects/Unit Control Chart
Individual/Moving Range Control Chart
p Chart
SPC Chart Interpretation
SPC (Special Applications)
Acceptance Control Chart
Average/Range Control Chart with Variable Subgroups
Chi-Square Control Chart
Demerit/Unit Control Chart
Exponentially Weighted Moving Average
Individual-Median/Range Control Chart
Multivariate Control Chart
p′ Chart and u′ Chart for Attributes (Laney’s)
Short-Run Attribute Control Chart
Short-Run Average/Range Control Chart
xvi Preface
Short-Run Individual/Moving Range Control Chart
Zone Format Control Chart
Process Improvement
Designed Experiments
Evolutionary Operation
Sequential Simplex Optimization
Sequential Simplex Optimization, Variable Size
Taguchi Loss Function
Reliability
Accelerated Reliability Testing
Reliability
Weibull Analysis
Comparative Data Analysis
Chi-Square Contingency and Goodness-of-Fit
Nonparametric Statistics
F-test
Hypothesis Testing
Testing for a Normal Distribution
Wilcoxon Rank Sum
Acceptance Sampling Plans
Acceptance Sampling for Attributes
Acceptance Sampling for Variables
While this reference does not exhaust the list of applicable techniques and tools to improve
quality, it is hoped that those included will provide the reader with a more in-depth under-
standing on their use.
Mark L. Crossley, M.S., C.M.I., C.Q.E., C.R.E.,
C.Q.A., C.Q. Mgr., C.S.S.B.B., Master B.B.
Quality Management Associates, Inc.
Contents
Usage Matrix Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Accelerated Reliability Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Temperature-Humidity Bias Accelerated Testing . . . . . . . . . . . . . . . . . . . . . . . . 5
Example of the Temperature-Humidity Acceleration Model . . . . . . . . . . . . . 5
Graphical Method for the Determination of the Energy of Activation Ea . . . . . 6
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Acceptance Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Modified Control Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Acceptance Control Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Acceptance Sampling for Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Operating Characteristic Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
MIL-STD-105E (ANSI/ASQC Z1.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Format for Use and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Continuous Sampling Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
CSP-1 Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
CSP-2 Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
AMethod for Selecting the AQL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Acceptance Sampling for Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Sampling Plans Based on Specified AQL, RQL, α Risk, and β Risk . . . . . . . 37
Sampling Plans Based on Range R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Average/Range Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Average/Range Control Chart with Variable Subgroups . . . . . . . . . . . . . . . . . 51
Average/Standard DeviationControl Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
v
vi Contents
Chart Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Variables Control Charts: Individuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Variables Control Charts: Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
What about Subgroup Size for the Variables Control Charts? . . . . . . . . . . . 71
Attribute Chart: p Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
For P ≤ 0.10, Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
For P > 0.10, Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Chi-Square Contingency and Goodness-of-Fit . . . . . . . . . . . . . . . . . . . . . . . . . 83
Chi-Square Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Goodness-of-Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Goodness-of-Fit to Poisson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Goodness-of-Fit for the Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 89
Goodness-of-Fit for Any Specified Distribution . . . . . . . . . . . . . . . . . . . . . . . . 89
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Chi-Square Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Confidence Interval for the Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Confidence Interval, n ≤ 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Confidence Interval, n > 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Confidence Limit, n > 30, Single-Sided Limit . . . . . . . . . . . . . . . . . . . . . . . . 102
Confidence Limit, n ≤ 30, Single-Sided Limit . . . . . . . . . . . . . . . . . . . . . . . . 103
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Confidence Interval for the Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Confidence Interval for the Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . 115
Testing Homogeneity of Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Defects/Unit Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Demerit/Unit Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Designed Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Normal Probability Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Visualization of Two-Factor Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fractional Factorial Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Calculation of Main Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Contents vii
Two-Factor Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Statistical Significance Based on t-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Variation Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Empirical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Testing Curvature or Nonlinearity of a Model (and Complete Case Study) . .172
An Alternative Method for Evaluating Effects Based on Standard Deviation . .178
Plackett-Burman Screening Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
The Normal Distribution as an Approximation of the Binomial . . . . . . . . . . . 192
Pascal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Cumulative Distribution Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Evolutionary Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Exponentially Weighted Moving Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
F-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Single-Sided vs. Double-Sided Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Example of a Frequency Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Formulation of the Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Conclusions and Consequences for a Hypothesis Test . . . . . . . . . . . . . . . . . . 224
Selecting a Test Statistic and Rejection Criteria . . . . . . . . . . . . . . . . . . . . . . . 225
Hypothesis about the Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Individual-Median/Range Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Individual/Moving Range Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Measurement Error Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Variables Measurement Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Terms and Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Combined (Gage) Repeatability and Reproducibility Error (GR&R) . . . . 264
Consequences of Measurement Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Confidence Interval for Repeatability, Reproducibility, and Combined R&R . .265
viii Contents
Confidence Interval for Repeatability, EV . . . . . . . . . . . . . . . . . . . . . . . . . 266
Confidence Interval for Reproducibility, AV . . . . . . . . . . . . . . . . . . . . . . . . 268
Confidence Interval for Combined Repeatability and Reproducibility, R&R . .269
Attribute and Visual Inspection Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
AMethod for Evaluating Attribute Inspection . . . . . . . . . . . . . . . . . . . . . . . . 272
1. Correct, C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
2. Consumer’s Risk, Cr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
3. % Manufacturer’s Risk, Mr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
4. Repeatability, R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5. Bias, B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .279
Multivariate Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
T2 Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Calculation of Individual and Average Covariance . . . . . . . . . . . . . . . . . . 284
Calculation of Individual T2Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Calculation of the Control Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Standard Euclidean Distance D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
E
Plotting Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Control Limits and Center Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Nonnormal Distribution C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
pk
C Adjusted for Sk and Ku Using Normal Probability Plots . . . . . . . . . . . . . 310
pk
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Nonparametric Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Comparing Two Averages: Wilcoxon-Mann-Whitney Test . . . . . . . . . . . . . . . 313
Comparing More Than Two Averages: The Kruskall-Wallis Rank Sum Test . . . 316
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
Reporting the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
p Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Using the p Chart When the Proportion Defective Is Extremely Low
(High-Yield Processes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
Exponential Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
Data Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
p' Chart and u' Chart for Attributes (Laney’s) . . . . . . . . . . . . . . . . . . . . . . . . 345
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Pareto Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361