Process quality control : troubleshooting and interpretation of data

667 Pages·2005·5.13 MB·English

by  Neubauer, Dean V., Schilling, Edward G., Ott, Ellis Raymond

Process Quality Control
Troubleshooting and
Interpretation of Data
Fourth Edition
Ellis R. Ott
Edward G. Schilling
Dean V. Neubauer
ASQ Quality Press
Milwaukee,Wisconsin
American Society for Quality,Quality Press,Milwaukee 53203
©2005 by ASQ
All rights reserved. Published 2005
Printed in the United States of America
12 11 10 09 08 07 06 05 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Ott,Ellis R. (Ellis Raymond),1906–
Process quality control :troubleshooting and interpretation of data / Ellis R. Ott,
Edward G. Schilling,Dean V. Neubauer.—4th ed.
p. cm.
Includes bibliographical references and index.
ISBN 0-87389-655-6 (hard cover,case binding :alk. paper)
1. Process control—Statistical methods. 2. Quality control—Statistical methods.
I. Schilling,Edward G.,1931– II. Neubauer,Dean V. III. Title.
TS156.O86 2005
658.5'62—dc22 2005010988
ISBN 0-87389-655-6
No part of this book may be reproduced in any form or by any means,electronic,mechanical,
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To Virginia, Jean, and Kimberly with love and appreciation.
About the Authors
T
he late Ellis R. Ott was professor emeritus of experimental statistics at Rutgers,
The State University of New Jersey, and the founding director of the Rutgers
Statistics Center. He received his PhD from the University of Illinois. He
consulted extensively, including work with the U.S. State Department and the United
Nations. Dr. Ott was the recipient of numerous quality control awards,including hon-
orary member of the American Society for Quality and its Brumbaugh Award, the
Eugene L. Grant Award,and the Shewhart Medal. He was honored by an award estab-
lished in his name by the Metropolitan Section of ASQ.
Dr. Edward G. Schilling is professor emeritus of statistics and former director of the
Center for Quality and Applied Statistics in the College of Engineering at Rochester
Institute of Technology. He was previously manager of the Lighting Quality Operation
of the General Electric Company. He received his MS and PhD degrees in statistics
from Rutgers University, where he studied under Ellis Ott. Dr. Schilling is a fellow of
the American Statistical Association,ASTM International,and the American Society for
Quality, and is the first person to win the American Society for Quality’s Brumbaugh
Award four times. He is also a recipient of the Shewhart Medal,the Ellis R. Ott Award,
Eugene L. Grant Award, Distinguished Service Medal from ASQ, and the Award of
Merit from ASTM International. He is the author of Acceptance Sampling in Quality
Control and was associate editor of the fifth edition of Juran’s Quality Handbook.
Dean V. Neubauer is employed at Corning Incorporated where he holds the appointed
position of senior engineering associate—statistical engineering,and holds multiple U.S.
patents and trade secrets. He is also an adjunct professor at the Center for Quality and
Applied Statistics in the College of Engineering at Rochester Institute of Technology.
Mr. Neubauer received a BS degree in statistics from Iowa State University and an MS
degree in applied and mathematical statistics from Rochester Institute of Technology. He
has actively participated on ISO and ASTM standards committees. He is a fellow and a
617
618 About the Authors
charter statistician of the Royal Statistical Society,and a member of the American Statis-
tical Association. He is a fellow and certified quality engineer of the American Society
for Quality, as well as the past chair of the Chemical and Process Industries Division.
He is also a book reviewer for Technometrics.
List of Figures and Tables
Table 1.1 Mica thickness,thousandths of an inch. . . . . . . . . . . . . . . . . 4
Figure 1.1 Thickness of mica pieces shown as a histogram. . . . . . . . . . . . 4
Figure 1.2 A normal distribution (with m= 0). . . . . . . . . . . . . . . . . . . 6
Figure 1.3 A lognormal distribution. . . . . . . . . . . . . . . . . . . . . . . . 7
Figure 1.4 A bimodal distribution composed of two normal distributions. . . . . 7
Table 1.2 Data:mica thickness as a tally sheet. . . . . . . . . . . . . . . . . . 9
Table 1.3 Mica thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 1.5 Two normal distributions with m = m but s > s. . . . . . . . . . . 13
1 2 2 1
Figure 1.6 Mica thickness; accumulated percents plotted on normal
probability paper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Table 1.4 Data:depth of cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 1.7 Depth of cut on normal probability paper. . . . . . . . . . . . . . . . 22
Figure 1.8 Distributions sampled by Shewhart:(a) rectangular parent
population; (b) right-triangular parent population; (c) normal
parent population. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Figure 1.9 Estimating percent of a normal curve outside given specifications. . . 26
Figure 1.10 Estimating confidence intervals of unknown process average. . . . . 28
Table 1.5 Mica thickness data in subgroups of n = 5 with their averages
g
and ranges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
–
Figure 1.11 Mica thickness, X and R charts; data in order as in Table 1.5. . . . . 33
Table 1.6 Values of the constant d. .. . . . . . . . . . . . . . . . . . . . . . 34
2
Figure 1.12 Schematic of a tobogganing production process. . . . . . . . . . . . 35
Figure 1.13 Stem-and-leaf of mica data means. . . . . . . . . . . . . . . . . . . 38
Figure 1.14 Ordered stem-and-leaf diagram of mica data. . . . . . . . . . . . . . 38
Figure 1.15 Form of box plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
xiii
xiv List of Figures and Tables
Figure 1.16 Ordered stem-and-leaf diagram of 40 individual mica
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Figure 1.17 Box plot of mica individuals and means. . . . . . . . . . . . . . . . 39
Figure 1.18 Box plot of 200 mica measurements. . . . . . . . . . . . . . . . . . 40
Figure 1.19 Dot plot of 200 mica thickness measurements and 40
subgroup means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Table 1.7 Electrical characteristics (in decibels) of final assemblies from
11 strips of ceramic:Case History 15.1. . . . . . . . . . . . . . . . . 48
Table 1.8 Air-receiver magnetic assembly:Case History 2.1. . . . . . . . . . . 49
Figure 2.1 Measured time for sand to run through a 3-minute egg timer
(recorded in order of observation). . . . . . . . . . . . . . . . . . . . 52
Figure 2.2 An egg timer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Figure 2.3 Twelve averages showing six runs above and below the median. . . . 57
Figure 2.4 Gross average weights of ice cream fill at 10-minute intervals. . . . . 57
Table 2.1 A comparison of the expected number of runs and the
observed number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Table 2.2 Critical extreme length of a run-up or a run-down in a random
set of kobservations (one-tail). . . . . . . . . . . . . . . . . . . . . 61
Figure 2.5 Control chart of mica thickness data with limits. . . . . . . . . . . . 64
–
Table 2.3 Factors to use with X and Rcontrol charts for variables. . . . . . . . 65
Figure 2.6 Matching a hole in a brass piece with diaphragm assembly. . . . . . 68
Table 2.4 Data:air-receiver magnetic assembly (depth of cut in mils). . . . . . 69
–
Figure 2.7 Control chart (historical) of X and Ron depth of cut. . . . . . . . . . 70
–
Figure 2.8 Comparing sensitivities of two X charts,n = 4 and n = 9
g g
with operating-characteristic curves. . . . . . . . . . . . . . . . . . . 73
Table 2.5 Computation of OC curve and average run length for Shewhart
–
X control chart with sample size n = 4. . . . . . . . . . . . . . . . . 75
g
–
Figure 2.9 Average run length curve for X chart with n = 4. . . . . . . . . . . . 75
g
Figure 2.10 Distributions with their associated distributions of averages
(n = 4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
g
Figure 2.11 Operating-characteristic curves of three decision plans associated
–
with an X control chart,n = 4. . . . . . . . . . . . . . . . . . . . . 77
g
Figure 2.12 Accumulated analyses from hourly samples over two weeks’
production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Figure 2.13 A control chart (historical) of chemical concentration of data
taken about once an hour over a two-week period (sample averages
and ranges of four consecutive analyses). . . . . . . . . . . . . . . . 79
Table 2.6 Data:gross weights of ice cream fill in 2.5-gallon containers. . . . . 80
Figure 2.14 A control chart (historical) of filling weights of ice cream
containers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Table 2.7 Gross weights of ice cream fill in 2.5-gallon containers. . . . . . . . 83
List of Figures and Tables xv
Table 2.8 Computations basic to a control chart test set calibration. . . . . . . 86
Figure 2.15 A control chart guide to test-set adjustments. . . . . . . . . . . . . . 86
Table 2.9 A performance comparison of six test sets over three
time periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Table 2.10 Part diameter for nine hours of production. . . . . . . . . . . . . . . 89
Table 2.11 Diameter of initial sample of fifty successive parts. . . . . . . . . . . 89
Table 2.12 Record of filling isotonic solution with averages and
ranges computed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . CD
Table 2.13 Subgroups of four across needles with averages and
ranges computed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . CD
Figure 2.16 Plot of hourly diameter readings shown in Table 2.10. . . . . . . . . 90
Figure 2.17 A diameter trend chart developed by the least squares method for
subsequent runs using a forced intercept. . . . . . . . . . . . . . . . 94
Figure 2.18 Control charts for data of Table 2.12. . . . . . . . . . . . . . . . . . CD
Figure 2.19 Control charts for data of Table 2.13. . . . . . . . . . . . . . . . . . CD
Figure 2.20 Digidot plot for subgroup mean data of Table 1.5. . . . . . . . . . . 96
Table 3.1 Record of chemical analyses (column 1) made on consecutive
batches of a chemical compound. . . . . . . . . . . . . . . . . . . . 100
–
Figure 3.1 An X and Rcontrol chart analysis of data. . . . . . . . . . . . . . . 101
Figure 3.2 Individual batch analyses showing two outages. . . . . . . . . . . . . 102
Table 3.2 Estimating sfrom a moving range. . . . . . . . . . . . . . . . . . . 103
Figure 3.3 A chart check for an outlier. . . . . . . . . . . . . . . . . . . . . . . 104
Figure 3.4 Data with two suggested outliers on the same end. . . . . . . . . . . 106
Table 4.1 Factors c to give an unbiased estimate. . . . . . . . . . . . . . . . . 110
4
–
Table 4.2 Statistical efficiency ofsˆ= R/d in estimating the
2
population parameter from ksmall samples. . . . . . . . . . . . . . . 111
Table 4.3 Data:breaking strength of single-fiber yarn spun on two machines. . 115
Figure 4.1 Breaking strength of single-fiber yarn from two machines. . . . . . . 115
Table 4.4 Data:measurements of transconductance of two groups of
electronic devices made from two batches (melts) of nickel. . . . . . 117
Figure 4.2 Transconductance readings on electronic devices from two batches
of nickel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Figure 4.3 Evidence of increased process variability. . . . . . . . . . . . . . . . 120
Table 4.5 Variability (as measured by ranges,r= 3) of two methods of
chemical analysis using four analysts. . . . . . . . . . . . . . . . . . 121
Table 4.6 Summary:estimating variability. . . . . . . . . . . . . . . . . . . . 124
Table 5.1 Probabilities Pr(x) of exactly xheads in 10 tosses of an
ordinary coin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Figure 5.1 Probabilities of exactly xheads in 10 tosses of an ordinary coin
(n= 10,p= 0.50). . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
xvi List of Figures and Tables
Table 5.2 Probabilities of exactly xoccurrences in n= 75 trials and p= 0.03. . . 131
Figure 5.2 Probabilities of exactly xdefectives in a sample of 75 from an
infinite population with p= 0.03. . . . . . . . . . . . . . . . . . . . 131
Figure 5.3 A control chart record of defective glass bottles found in
samples of 120 per shift over a seven-day period. . . . . . . . . . . . 135
Figure 5.4 cchart on stoppages of spinning frame. . . . . . . . . . . . . . . . . 142
Figure 5.5 uchart on stoppages of spinning frame. . . . . . . . . . . . . . . . . 143
Figure 5.6 Form to record inspection by attributes. . . . . . . . . . . . . . . . . 144
Figure 5.7 A control chart using attributes data; visual inspection of a
TV component. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CD
Figure 5.8 Plot of average gram weight of n= 3 tubes/sample taken at
15 minute intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Table 6.1 Probabilities P of finding x≤2 in a sample of n = 45 for
A
different values of p. . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Figure 6.1 Operating-characteristic curve of a single sampling plan for
attributes (n= 45,c= 2). . . . . . . . . . . . . . . . . . . . . . . . . 157
Figure 6.2 Averaging outgoing quality (AOQ) compared to incoming percent
defective Pfor the plan n= 45,c= 2. . . . . . . . . . . . . . . . . . 159
Table 6.2 Average outgoing quality (AOQ) of lots proceeding past an
acceptance sampling station using the plan n =45,c =2. . . . . . . 161
Figure 6.3 Lot-by-lot record for acceptance sampling (single sampling). . . . . 165
Table 6.3 OPQR:outgoing product quality rating—weekly summary. . . . . . CD
Table 6.4 Computation of standard quality demerit level and control limits
–––
(QD and s) per n units. . . . . . . . . . . . . . . . . . . . . . . . . CD
n n
Figure 6.4 An OPQR control chart showing control limits. . . . . . . . . . . . . CD
Table 6.5 Steps in producing an enameled basin. . . . . . . . . . . . . . . . . 168
Figure 6.5 Representation of steps in metal fabrication to form an
enameled basin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Figure 6.6 An enameled basin. . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Table 6.6 Daily inspection sheet (sampling). . . . . . . . . . . . . . . . . . . . 170
Table 6.7 Enamel basins—defect analysis after four days. . . . . . . . . . . . . 171
Figure 6.7 Tripod supporting 16-cm enameled basin during firing. . . . . . . . 172
Table 6.8 Summary showing percentage of major defects over four
time periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Figure 6.8 Summary of percent classification of 16-cm enameled basins
over four sampling periods. . . . . . . . . . . . . . . . . . . . . . . 173
Table 6.9 Changes in quality classification over four time periods. . . . . . . . 174
Table 6.10 Record of weaving defects—major and minor—found in cloth
pieces over two days (from five looms on two shifts). . . . . . . . . 177
List of Figures and Tables xvii
Figure 6.9 Record of percent major damaged cloth in March and April
following start of quality control program. . . . . . . . . . . . . . . 180
Figure 6.10 Definition of tsfor NL gauge. . . . . . . . . . . . . . . . . . . . . . 181
Figure 6.11 Some operating characteristics of NL-gauging plans and a
–
variables control chart on X with n = 4. . . . . . . . . . . . . . . . 183
g
Figure 6.12 Molded plastic bottle components. . . . . . . . . . . . . . . . . . . . 184
Figure 6.13 Adjustment chart on a screw machine operation using
NL-gauging principles. . . . . . . . . . . . . . . . . . . . . . . . . . 187
Figure 6.14 Deriving an OC curve for an NL-gauging plan (general procedure). . 189
Table 6.11 Derivation of operating-characteristic curves for some
NL-gauging plans with gauge compressed by 1.0s(t= 1.0). . . . . . 189
Figure 6.15 OC curves of NL-gauging plan. . . . . . . . . . . . . . . . . . . . . 189
Table 6.12 Percent of normally distributed product outside 3s specification
from nominal mean of control chart for comparison of NLG to
other control chart procedures. . . . . . . . . . . . . . . . . . . . . . 190
Table 6.13 Deriving an OC curve for the NLG plan n= 4,t= 1.2,c= 1. . . . . 190
Figure 7.1 Statistical process quality control. . . . . . . . . . . . . . . . . . . . 196
Table 7.1 Factors for Shewhart charts,n= n. . . . . . . . . . . . . . . . . . . 198
g
–
Table 7.2a Factors for conversion of X chart into median chart. . . . . . . . . . 201
–
Table 7.2b Factors for conversion of X chart into midrange chart. . . . . . . . . 201
Table 7.3 Mean,median,range,and standard deviation of mica thickness. . . . 202
Figure 7.2 Median chart for mica thickness. . . . . . . . . . . . . . . . . . . . 203
Figure 7.3 schart for mica thickness. . . . . . . . . . . . . . . . . . . . . . . . 204
Figure 7.4 Acceptance control chart for mica thickness. . . . . . . . . . . . . . 208
Figure 7.5 Modified control limits. . . . . . . . . . . . . . . . . . . . . . . . . 211
Figure 7.6 Moving average chart for mica thickness. . . . . . . . . . . . . . . . 216
Figure 7.7 Geometric moving average chart for mica thickness. . . . . . . . . . 216
Figure 7.8 CUSUM chart for mica thickness,d= 1.58,q= 45°. . . . . . . . . . 217
Figure 7.9 V-mask. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Figure 7.10 Kemp cumulative sum chart. . . . . . . . . . . . . . . . . . . . . . . 224
Figure 7.11 One-sided cumulative sum chart. . . . . . . . . . . . . . . . . . . . 225
Figure 7.12 CUSUM chart equivalent to Shewhart chart. . . . . . . . . . . . . . 226
Figure 7.13 Snub-nosed CUSUM mask. . . . . . . . . . . . . . . . . . . . . . . 227
Table 7.4 Average run length for special CUSUM charts. . . . . . . . . . . . . 228
Figure 7.14 Precontrol justification. . . . . . . . . . . . . . . . . . . . . . . . . 230
Table 7.5 Precontrol rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
Figure 7.15 Precontrol schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . 231