Mistakes in Mistakes in and How to Fix Them

124 Pages·2021·14.414 MB·English

by  Donald W. Benbow

Mistakes in
Mistakes in
and How to Fix Them
Donald W. Benbow
ASQ Quality Press
Milwaukee, Wisconsin
Mistakes in Quality Statistics and How to Fix Them
© 2021 by Donald W. Benbow
All rights reserved. Published 2021
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Publisher’s Cataloging-in-Publication data
W. Benbow.
Description: Includes bibliographical references. | Milwaukee, WI: Quality
Press, 2Tial.
Title: Mistakes in quality statistics and how to fix them / by Dona
DeWsc.rBipetniobno:wI.ncludes bibliographical references | Milwaukee W
P 2021 ,
IIdde nrettiisffsiie, rs: LLCC. CCNN: 22002211993355779922 || IISSBBNN: 997788-11-6633669944-000000-77 ((pabperb
General
uMjeetchtso:dology |taAtusdt ictsin. g| |taQtusalt citsy—covnatroulat|oBnI.S|ACtaBtUsStIcNs—ES
ECONOMICS / Auditing | MATHEMATICS / Probability & St
Clasesnifeicraation: LCC QA276 .B46 2021| DDC 519.5—dc23
prior written permission of the publisher.
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800-248-19A46tt eonrt bioono [email protected],. wholesalers, schools, and corporations: Qua
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About the Author
For nearly 30 years, Don Benbow has conducted industrial sta­
tistics courses for employees of approximately 100 companies,
both face to face and through ICN, Iowa's closed-circuit fiber
For nearly 30 years, Don Benbow has conducted indus
tistics courses for employees of approximately 100 co
both face to face and through ICN, Iowa’s closed-circ
optics TV network. Previously, he taught mathematics,
and freshman engineering courses at Marshalltown Co
College. He holds BS and MS degrees in mathematics fr
State University and Michigan State University, respect
is co-author of The Certified Quality Technician Handbook,
tified Six Sigma Black Belt Handbook, and Introduction to
lem Solving, all available from ASQ Quality Press. He is
123
List of Figures and Tables
FIGURES
Figure 1.1 Graph of the data from Example 1.1................... 2
FIGURES
Figure 1. 1 Graph of the data from Example 1.1
Figure 1. 2 Graph of the data from Example 1.2
Figure 1. 3 Graph of the data from increased
sample sizes....................................
Figure 1. 4 The distribution of hole sizes showing
standard deviation boundaries and
specification limits ......................
_ f e, x x .............................
tail 005 shaded
Figure 2. 1 Spot-welder diagram with strength data ...
Figure 2. 2 Graph of spot-weld strength data..................
Figure 2. 3 Regression line plotted with data points.....
linear correlation coefficient.................................... 17
Figure 2. 4 Graph of the data from Example 2.2 ............
Figure 2. 5 Elixnaemarpcloersroeflavtiaorniocuosevffailcuieenstof the
Figure 2. 6 Graph of data from Table 2.3..................................
FFiig ure 22.7 7 GGrahph off ddatta ffr om TTabbll e 22.44..................................
Figure 2. 8 Fermentation tank with beer well .......................
Figure 2. 9 Graph of data with beer well temperature
set at 140° .........................................
Figure 2.1 0 Sketch for Example 2.5.........................................
Figure 2.1 1 Plot of data from Table 2.5 ..................................
viii Mistakes in Quality Statistics
Figure 2.1 2 Scatter diagram for the data in Table 2.6.............. 26
Figure 2.V3 Comparing predktedwithactual DE values .. 29
Figured AcnfirolcntrttOowinyinttehiliOy....................... 42
Figure 4.2 Control chart without indicators
ofm3fability..................................................................... eet
Figure 4.3 Histogram showing three distinct humps . . . . 45
Figuie 4.f Ctntitl chnit withtut indicnttis
3icuie i.3 Histtciny shtsinc thiee distingt huyps ...
3icuie i.i Ctntits ghnit fti iypitved pitgess ....................
3icuie i.5 Histtciny shtsinc the dntn nftei pitgess
iypitveyent .................................
3icuie i.6 3ive-b.-eicht niin.s tf ghtgtsntes tn n
snxed-pnpei-gtveiedgtnve.ti..........................
3icuie i.7 Tst yethtds fti sesegtinc five ghtgtsntes
3icuie i.8 Individunss gtntits ghnit........................................
3icuie i.9 X-bni nnd R ghnit fti n bntgh pitgess ..............
3icuie i.n0 X-MR gtntits ghnit usinc nveince vnsues
3icuie i.nn Sgnttei pstt tf the dntn in Tnbse i.n.....................
3icuie i.nf Sgnttei pstt tf the ptints in Tnbse i.f .................
3icuie i.n3 X-bni nnd R ghnit usinc stintified dntn .............
3icuie i.ni Histtciny tf the iendincs in 3icuie i.n3 .......
3icuie i.n5 Issustintitn tf t.pigns pie-gtntits siyits ..........
3icuie i.n6 Pie-gtntits ghnit fti Exnypse i.7 sith ftui
snypes.............................................
3icuie i.n7 Issustintitn fti Exnypse i.n0 .................................
3icuie i.n8 Issustintinc the spegifigntitn siyits in
teiys tf stnndnid devintitns fity the
pitgess yenn ................................................................
3icuie i.n9 Ntiyns distiibutitn, sith the ptititn
stf epgiitfidguntgittitnnsityhnitt svhintdsnetdes the stsei
Figure 4.22 Illustrating a centered process............................... 70
List of Figures and Tables ix
Figure 4.23 Excel function NORMSDIST with -3.705
input..................................................... ab
Figure 6.1 Graphical representation of the average
Figure 4.23 Excel function NORMSDIST with -3.705
input ..................................................
Figure 6.1 Graphical representation of the average
Figure 7.1 Example of an acceptance sampling plan.......
Figure 7.4 Examples of ОС curves............................................. 98
Figure 7. 2 Example of a double sampling plan...............
Figure 7. 3 Example of sampling plan that uses arrows..
Figure 7. 4 Examples of OC curves ......................................
Figure 7. 5 OC curve for 1.5 AQL...........................................
Figure 7. 6 Details for an OC curve for 1.5 AQL ............
Figure 7. 7 Ideal OC curve for an QAQL = 1.5% .................
Figure 7.8(a) Example of an OC curve for AQL = 1.5 ............
Figure 7.8(b) Another example of an OC curve
for AQL = 1.5 ..................................
Figure 7. 9 Table for converting Q-values to percent
defective...........................................
Table 1. 1 Partial %2 table............................................................ 9
TABLES
Table 2. 2 EsbrnalePdtnsibesusing the regression
equation............................................................................ 16
Table 2. 3 Data relating COtconcentration
togrowtErate
iquotion tttttttttttttttttttttttttttttttt
Tobli et3 Doto riloting COe concintrotion
to growth roti ttttttttttttttttttttttttttt
Tobli et4 Doto for 18 botchis onc corrilotions
wt tttttttttttttttttttttttttttttttt
Tobli et5 Frocturi coto for Exoepli et5tttttttttttttt
Tobli et6 Doto riloting orifici cioeitir
Table 4. 1 Data points for Example 4.5................................ 55
X Mistakes in Quality Statistics
Table 4. 2 Values from Table 4.1 compared
with lagl values............................. 56
Table 4. 3 Illustrating batch means for batch size n=8... 58
Table 4.2 Values from Table 4.1 compared
Table 4.3 Illustrating batch means for batch size n = 8..
Table 6.1 A23 factorial data collection sheet for
Table 4.4 Values of d2 for several sample sizes
Table5.1 d2 for small numbers of subgroups
Table6. 1 A23 factorial data collection sheet for
Example 6.1 ....................................
Table6. 2 A23 factorial data collection sheet with
run averages ..................................
Table6. 3 A23 full factorial design using the
+ and - format ................................
Table6.4 A23 full factorial desin showin
interaction coumns ...................................................
Preface
This book began as a presentation titled "Caveats Regarding
the Use of Statistics" that I made during the May 2009 World
Quality Conference. It is not intended to serve as a statistics
This book began as a presentation titled “Caveats R
the Use of Statistics” that I made during the May 200
Quality Conference. It is not intended to serve as a
textbook. In fact, it assumes the reader has some familia
the subject, perhaps through an introductory course. T
courses tend to emphasize how to perform statistical
and give little attention to errors that can occur in the
xi