IS 397-1: Method for Statistical Quality Control During Production, Part 1: Control Charts for Variables

29 Pages·2003·2.3 MB·English

by  Bureau of Indian Standards

इंटरनेट मानक
Disclosure to Promote the Right To Information
Whereas the Parliament of India has set out to provide a practical regime of right to
information for citizens to secure access to information under the control of public authorities,
in order to promote transparency and accountability in the working of every public authority,
and whereas the attached publication of the Bureau of Indian Standards is of particular interest
to the public, particularly disadvantaged communities and those engaged in the pursuit of
education and knowledge, the attached public safety standard is made available to promote the
timely dissemination of this information in an accurate manner to the public.
“जान1 का अ+धकार, जी1 का अ+धकार” “प0रा1 को छोड न’ 5 तरफ”
Mazdoor Kisan Shakti Sangathan Jawaharlal Nehru
“The Right to Information, The Right to Live” “Step Out From the Old to the New”
IS 397-1 (2003): Method for Statistical Quality Control
During Production, Part 1: Control Charts for Variables
[MSD 3: Statistical Methods for Quality and Reliability]
“!ान $ एक न’ भारत का +नम-ण”
Satyanarayan Gangaram Pitroda
““IInnvveenntt aa NNeeww IInnddiiaa UUssiinngg KKnnoowwlleeddggee””
“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता हहहहै””ै”
Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”

IS 397 (Patt 1) :2003
W?dkmFm

ml
Indian Standard
METHODS FOR STATISTICAL QUALITY
CONTROL DURING PRODUCTION
PART 1 CONTROL CHARTS FOR VARIABLES
.
1
(Second Revision) ,
ICS03.120.30

0 BIS2003
BUREAU OF INDIAN STANDARDS
MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
NEW DELHI 110002

December 2003 Price Group 9
... ,,%.
!
Statistical Methods for Quality and Reliability Sectional Committee, MSD 3
FOREWORD
This Indian Standard (Part 1)(Second Revision) wasadopted bythe Bureau of Indian Standards, atler the draft
finalized by the Statistical Methods for Quality and Reliability Sectional Committee had been approved by the
Management and Systems Division Council.
Controlling the quality ofproducts soastomaintain itatagiven level isamajor problem with allthe producers.
Fromtheearlydaysofindustrial production manufacturers havetried tousethesamemen,machines andmethods
and similar raw materials inthe hope of turning out products ofuniform quality. But neither men nor machines
are infallible and causes of irregularity often creep inadvertently. Asaresult, rejections infinished materials are
rarely eliminated and inspection and screening become necessary to varied extents determined by the nature of
the product and the goodwill and policy of the manufacturer.
Sincescreening isnot aneffective control, thequestion remained alively issuewith the production management
andvarious systemsofcontrol weredevised fromtime-to-time. In 1924Dr. W.A. Shewhart oftheBellTelephone
Laboratories, USA developed the control chart method of controlling the quality during production which is
meant to be an integral part of the production process, This technique based on statistical methods, however,
does notprovide anautomatic corrective action inthewaymechanical or electrical systems do. Instead, itgives
awarning signal to the operator that hemust take here and nowthe corrective action on his machine or process
to ensure maintenance of quality in further production. Its effectiveness, therefore, depends on the promptness
withwhichthewarning isheeded to andaction taken, keeping inviewthefactthat thework involved inapplying
themethod islargely basedonjudgement, knowledge oftheprocessandtechnical skill intracing downassignable
causes ofvariation to their source.
Thisstandard, wasoriginally published in 1952,waslargelyareproduction oftheAmerican Defence Emergency
Standard Z 1.3-1942 ‘Control chart method of controlling quality during production’ which had proved quite
useful inthe military stores purchases during second war. The first revision of this standard had been taken up
with aview to make the standard more comprehensive by including control charts for medians and mid-ranges
whicharequicker, easytooperate andatthesametimequiteefficient forsmallsamples. Further, themethodology
ofadopting control charts techniques for usewhenmanufacturing isundertaken to apredetermined specification
was also included. As the original standard was bulky, itwas split into two parts during this revision, namely,
Part 1dealing with control charts for variables and Part 2dealing with control charts for attributes.

This second revision ofthe standard has beentaken upto inc)ude:

a) difference between assignable causes and chance causes inatabular form,
b) choice of measuring equipment during the preliminaries to installation of control charts,
c) tiu-therguidance for deciding the frequency during the preliminaries to installation of control charts,
d) explanation for not considering lower control limit (LCZ,)for homogenization of range values in
R-chart and further necessary actions,
e) conditions under which modified control chart should not be used,
f) many editorial corrections, and
g) amendment issued to this standard at appropriate place.
Further inthis revision the text on process capability and itscomparison with the tolerance have been suitably
modified and reference has been given m 1S 10645 :2002 ‘Methods for estimation of process capability and
process performance’, isthe necessary adjunct to this standard.
Inaddition tothis Part 3, 1S397 has the four parts. The other parts are:
(Part O):2003 Guidelines for selection of control charts (#h-strevision)
(Part 2) :2003 Control charts for attributes (third revision)
(Part 3): 2003 Special control charts by variables (first revision)
(Part 4): 2003 Special control charts by attributes (first revision)
The composition of the Committee responsible for the formulation ofthis standard isgiven in Annex I).

-
*.” .. .
IS397 (part 1) :2003
Indian Standard
METHODS FOR STATISTICAL QUALITY
CONTROL DURING PRODUCTION
PART 1 CONTROL CHARTS FOR VARIABLES
(Second Revision)
1SCOPE ISNo. Title
applications: Part 2 Continuous
1.1Thisstandard(Part 1)outlinesthemethodofcontrol
models (first revision)
chart by variables for controlling the quality during
production. The principles of procedure pertaining to 10645:1998 Method for estimation ofprocess
control charts for individual observations, averages, capability (first revision)
medians, mid-ranges, ranges and standard deviations 5420 Guideonprecisionoftestmetho&
(Part 1): 1969 Principles and applications
are given ingeneral terms.
(Part 2): 1973 Inter laboratory testing
1.2 The standard also lays down the procedures for
3TERMINOLOGY
the construction of modified control charts which
can be usefully adopted when the manufacture is For the purpose of this standard the definitions given
undertaken to predetermined specifications. inIS 7920 (Part 1)and IS 7920 (Part 2) shall apply.
1.3 The principles of control charts have been 4BASICCONCEPTS UNDERLYING CONTROL
illustrated with a variety of examples. Certain broad CHART TECHNIQUE
guidelines astothe interpretation ofthe data resulting
4.1 Variation and ItsCauses
from control charts are also included.
In the repetitive making of a product so often met in
2REFERENCES
the present day industrial production, variation inany
The following standards contain provisions, which chosen quality characteristic is an ever present
through reference inthis text constitute provisions of phenomenon. Although such variation may be due to
this standard. At the time of publication, the editions a variety of causes and their interaction known and
indicated were valid. All standards are subject to unknown,which constantly influence theprocess, they

revision and parties to agreements based on this can be broadly classified into following two distinct

standard are encouraged to investigate the possibility categories:
of applying the most recent editions of the standards
a) Variation due to assignable causes, such as,
indicated below:
different settings of a machine, different
1SNo. Title batches of raw materials that are being fed,
7920 Statistical vocabulary and andchanges inoperators whohavetien over
symbols: inanew shift.
(Part 1): 1994 Probability andgeneral statistical b) Variation due to chance (non-assignable or
terms (second revision) common) causeswhichareunavoidable inthe
(Part 2): 1994 Statistical qualitycontrol (second process due to such inherent variation that
revision) existinrawmaterials, machines, atmospheric
9300 (Part 2): 1989 Statistical models for industrial conditions, etc.

,.. ~“..-
IS397 (Part 1): 2003
4.2 Difference Between Chance Causes and Assignable Causes
sl Chance (Non-assignable) Causes Assignable Causes
No.
(1) (2) (3)
i) Consists ofmany individual causes. Consists of one orjust afew individual causes.
ii) Any one chance cause results in a minute Any one assignable cause can result in a large
amount of variation (but many chance causes amount of variation.
acttogether toyield asubstantial total).
iii) Cannot economically be eliminated from a Can be detected. Action to eliminate the cause(s) is
process. usually economically justified.
iv) When only chance cause is present, the If assignable variation is present the process isnot
process isoperating at itsbest. operating at itsbest.
v) An observation within the control limits of An observation beyond control limitsusually means
random variation means the process should the process should be investigated and corrected.
not be adjusted.
vi) Under chance causes, the process is With assignable causes present, the process is not
sufficiently stable to use sampling procedures suftlciently stable to use sampling procedures for
to predict the quality of total production or prediction.
make process optimization studies.
4.3 Process Under Statistical Control from aprocess follow a statistical law inthe form of a
known distribution, if samples of given size are taken
Whennoassignable causes of variation arepresent in
fromthesameprocess atmore or lessregular intewals,
aprocess and itoperates only under asystem ofnon-
then sample statistic, such as average or standard
assignable or chance causes, the process issaid to be
deviation, also follow known distributions. Of course,
inastate of statistical control. Such variations due to
thisdistribution isnot thesameastheone obtained for
chance causes occur in a random fashion and are
theindividualobsewations fromtheprocess. Generally
usually found to obey certain statistical laws. If large
speaking the distribution of the sample statistics that
numberofobservations obtained fromaprocess,which
isunder astate ofstatistical control, are studied inthe aredealtwithinthisstandardareofthenormalorknown
form of afrequency distribution, itwill generally fall type whoseparameters canbe estimated.
into a bell shaped symmetrical pattern wherein most
4.5 Control Charts
of the observations cluster around the average value
4.5.1 The above mentioned behaviour of the sample
and fewer observations are found as one moves away

statistics obtaining fkoma process !nfluenced only by
from the average value.

random causes is the foundation on which the control
4.4 Normal Distribution chart technique is based. Essentially it is a graphical
4.4.1ThebelIshapedsymmetricpatternthatisobtained method representing a sequence (in time) of sample
by the observations emanating from a process under statistics.Itconsistsof a central line(CL)denotingthe
statistical control is generally well represented by the averagevalueofthestatisticbeingplottedandithastwo
normaldistribution.Thisdistributionischaracterizedby controllimitsoneithersideofthecentrallinewhichare
twoparameters,namelythemeanvalueandthestandard calleduppercontrol limit@VCLa)ndlowercontrollimit
deviation. It is symmetrical and 99,73 percent of the (LCL).Thecontrollimitsaredeterminedstatisticallyfrom
observationsliewithinthreestandarddeviationsfi-omthe theprobabilitydistributionofthesamplestatistic.
mean on both sides. Thus, less than 3 in a thousand
4.5.2 The purpose of control chart isto obtain astate
observationsareexpectedtofallbeyondthethreestandard
of statistical control by locating and eliminating the
deviations from the mean on both sides. For fiwther
assignable causes and then to maintain theproduction
description about the properties of this distribution,
in this state so as to ensure the manufacture of
attentionininvitedtoIS9300(Part2).Henceinaprocess
consistent products of acceptable quality. For this
understatisticalcontrolifanysinglemeasurementistaken
purpose the variation due to non-assignable causes is
and itdoesnotfallwithin*3CTtlom themean, itcanbe
estimated and then used asthe basis for the detection
regarded asnot belongingto that dkribution orto that
of the variation due to assignable causes by plotting
cause system and the presence of an assignable cause
thesample statistic onthecontrol chart. Aslongasthe
affectingtheprocessmaybeinferred.
plotted point iswithin thecontrol limits,theprocess is
4.4.2Justasalargenumberofindividualmeasurements lefl alone. However, if a point falls either below the

2
?..
“. *_
IS397 (part 1): 2003
lowercontrol limit or above the upper control limitor found within the sample items should be due to non-
depicts other unnatural pattern (see 7.2) there is a assignableorrandomcauseswhereasthevariationfound
possibility oftheexistence ofsomeassignable cause(s) between samples should be ascribable to some
and an investigation is made for taking action to assignable causes. The division ofthe production flow
eliminate such causes. insuchamannerthateachportionyieldsasamplehaving
this property is known as ‘rational sub-grouping’.
5 PRELIMINARIES TO THE INSTALLATION
A natural sub-group for example would be the output
OF CONTROL CHARTS
of a short time period since the variation in items
5.1 Choice of Quality Characteristic manufactured close to each other inthe time sequence
Tostartwith,adecision hastobetaken withregard to aremuch more likelyto represent chance fluctuations.
the quality characteristics for which a control
5.3.2 Theproblem offormingrational sub-groupsalso
programme is desired. Characteristics affecting the
depends onthe technical knowledge of the production
performance of the product should normally be the process and the familiarity with the conditions under
object of first attention. These may be the features of
whichtheproduct isto bemanufactured. Whereas itis
the materials used or components or parts of the
notpossibletogiveexact instructions fortheformation
products, forexample, tensile strength ofthecorewire
of rational sub-groups that will cover all cases, a few
ofcablesorthickness ofthe insulation. Sometimes the illustrations may be helpfhl in this direction. Thus, if
characteristic may be for the finished product as a
different machine settingshave aneffect onthequality
whole likethe life of incandescent lamps.
characteristicthatisbeingstudied,alltheunitsinasingle
sub-group should come from the same setting. Again,
5.2 Choice ofthe Place for Control
ifdifferent batches of material have an effect, then all
5.2.1 In any production process it is of utmost units inone sub-group should be from the samebatch.
importance that proper checks through control charts Extendingthis,itmaygenerallybeadvisablenottoform
areexercized atstrategic points. Topinpoint theplace sub-groups suchthat asingle sub-group willconsistof
for suchcontrols itisdesirable to determine the areas itemsmanufacturedindifferent shifts,fromcomponents
ofmaximum potential for return inthe form of direct obtained from different sources, from different
profits, reduction in scraps, increase in productivity, production lines, from different machines, moulds,
etc.Apropervalueanalysisofalltheperformance may operators, etc.Inmany situations asmallsampletaken
be quite helpful inthe context. intheorderofproduction meetstheprincipleofrational
sub-groups, sinceitislikelytorepresent theimmediate
5.2.2 Itmayalsobeworthwhiletostudytheproduction
state of the process at the time sample was selected.
process to determine the nature and location of the
However, itshould be noted that this isnot auniversal
causes that tend to give rise to deviations in the
recommendation.Ifoneisttilng samplefromamachine
characteristic chosen. The method of inspecting
with multiple spindles or multiple positions or heads,
individual article or produ ct for the selected
thenaseriesofconsecutive unitsfromthemachineasa
characteristic is equally important since factors like
whole will not form a rational sub-group capable of
inspection fatigue may give rise to errors in
studyingthe variation between the different heads.For
observations.Thus,irregularities evident inqualitydata
example, if a filling machine has six heads which
may arise from errors of inspection as well as from
simultaneously fill six consecutive containers in the
faults inthe production process. Errors in inspection
production line,theneverysixthunittaken(andnotthe
may result from a faulty test apparatus, faulty use of
consecutive six units) from the process will form a
otherwisecorrect apparatus, etc.Itisalsotobedecided
rational sub-group, becatisethe variations within such
beforehand whether the entire output of products
sub-groups would be the inherent variation due to the
should be considered as a single stream having a
heads andthe variation between the sub-groups would
common system of causes or as two or more distinct
be the variation obtaining from the different heads of
streams each to be treated separately in the control
the machine. In such situations, precise setting of the
programme because they come from different cause
sixheadsbecomes verycrucial.
systems such as different conveyor lines, different
machines or different shifts of workmen, etc. 5.3.3Toavoidbiasintheformationofrationalsubgroups,
the following two precautions must be taken in the
5,3 Choice of Rational Sub-groups
selectionof consecutivesamples:(a) periodic selection
5.3.1 Sincethebasicaimofcontrolchartsistoseparate shouldnot coincidewith any relevant-periodic features
the variation due to assignable and non-assignable intheprocess,and(b)selectionofsamplesshouldnotbe
causes, it is evident that each sample should be madeon a fixedtime schedule ifforeknowledgeofthe
representative of a homogeneous segment of the selectiontime would have an influence on the quality
production flow.Sointhe idealcondition thevariation characteristicofthearticleselected.

3
IS397 (Part 1) :2003
5.4 Frequency and Size of Samples tolerable depending uponthe application. Ifit exceeds
30 percent, the equipment should be regarded as
5.4.1Nogeneral rules maybe laiddown forfrequency
inappropriate. Inaddition, themeasurementuncertainty
of sub-groups. Each case must be decided on its own
ofthe measuring equipment should be much lessthan
meritsconsidering boththecostoftakingandanalyzing
the tolerance ofthe characteristic.
measurements and the benefits to be derived from
action based on control charts. Inthe initial useofthe 5.6 Choice of the Types of Control Charts
control chart for analyzing a process, it may be
In the case of measurable quality characteristics it is
desirable to arrive at conclusions quickly by taking
generally the common practice to maintain a pair of
frequent sampIes. Later on, if troubles have been
control charts — one for the control of average level
diagnosedandcorrected andthefunction ofthecontrol
of the process (average chart or median chart or
chart has become the maintenance of the process
mid-range chart) and the other for the control of
control on current production, it may be advisable to
reducethefrequency ofsampling. Asaguideline, sub- dispersion (range chart or standard deviation chart).
Of course, when a chart for individtial measurements
group frequencies for ongoing production monitoring
is maintained, there is no possibility of keeping the
could betwice per shift, hourly or some other feasible
companion chart for dispersion.
rate,however, interval between twosub-groups should
be half of the known duration of trouble free
6SETTING UP OF THE CONTROL CHART
performance.
6.1 Preliminary Data Collection
5.4.2 The sizeofthe sample to betaken depends ona
numberofpracticalconsiderations. However,generally After having decided upon the quality characteristic
speaking, largesamples taken atlessfrequent intervals whichistobecontrolled andthe frequency andsizeof
may detect a small shift in the process average more the sample to be taken, some initial inspection data
quickly, but small samples taken at more frequent has to be collected and analyzed for the purpose of
intervalswilldetect alarge shiftmore quickly. Inmost determining the central line and control limits of the
ofthe industrial use of the control charts, samples of static. The preliminary data may be colIected sample
size 4 or 5 are found to be quite common. A sample bysample(in sub-groups ofsize asdecided in5.4)till
sizeof5isrecommended sincethe computation ofthe about 25 samples are obtained from the continuous
average in this case can be considerably simplified. run ofthe production process. Care isto be exercised
Whenmedian charts are used, samples of size 3 or 5 during thecourse ofthis initial data collection thatthe
aremostconvenient since they avoid the computation process is not unduly influenced intermittently by
altogether for the calculation of the median value. In extraneous factors like change in the feed of raw
casethemid-range isused, then alsothecomputations materials, operators and machine settings.
are considerably simplified since the average of only
two observations (Iargest and smallest) are to be 6.2 Analysis of Preliminary Data

obtained. It may, however, be noted that the use of
6.2.1 Analysis of the preliminary data is undertaken

median or mid-range in place of average results in a
firstly by homogenizing the dispersion (range or
slight lossof efficiency but this loss ismarginal inthe
standard deviation) ofthevarious sub-groups andthen
case of small samples. Samples of smailer size may
by homogenizing the central tendency (such as
havetobeusedifthecostofmeasurements istoohigh.
average, median or mid-range). This order for
Inmostofthe chemical industries using batch process
homogenization process becomes necessary sincethe
the samples of size 1or 2 are frequently preferred. It
ranges (or standard deviation) also enter into the
may,however, benoted that larger the sample sizethe
calculations needed for homogenizing the averages.
moredesirable itistousethestandard deviation rather
than range as a measure of sub-group dispersions, 6.2.2 Homogenization for Dispersion
5.5 Choice of Measuring Equipment
6.2.2.1 Using range method
The measuring equipment used for measuring the test
Ifthe sample size chosen isnot more than 6, then for
results should be calibrated whose least count should
each of the sub-groups, the range (R) shall be first
bepreferably 1/1Ohoftolerance orprocess capability.
calculated and the average range value (~ ) shall be
The variation due to measuring system should be
computed from these ranges. Depending upon the
quantified and minimized [see IS 5420 (Part 1) and
IS 5420 (Part 2)]. This variation due to measuring samplesize,thevalueoffactor D1shallbechosenfrom
Annex A. Ifal!theranges are found to be lessthan or
system should be less than 10 percent of the total
process variation ofthe characteristic. Ifthis variation equaltoDd ~ theinitialdata collected shallbedeemed
is between 10 percent to 30 percent, it may still be tobe homogeneous and acceptable for the purpose of

4
..,...
IS397 (Part 1): 2003
further calculation ofthe control limits. Incaseoneor size. Ifanyoftheaverages are found to lieoutside the
more range valuesare foundtoexceedthevalueDq~, interval ~ ~ A2~ then the observations in the sub-
the observations inthesub-group corresponding tothis groups corresponding to these averages shall be
range shall be discarded. For the remaining data, the discarded. From the remaining data, a fresh grand
above procedure shall be repeated (that is, the average shall be computed and the above procedure
calculation of the new average range R and shall be repeated till all the average values are found
comparison of all the remaining ranges with D~ ~ ) to lie within Y k Az ~. In case the data has earlier
been homogenized by using standard deviation
tilalllthe range values are lessthan DA~.
(see 6.2.1.2), then instead of A2~ the quantity Al F
6.2.2.2 Using standard deviation method
shall be used in the above homogenization process
In case the sample size chosen is fairly large, it is where the factor A~is suitably chosen tlom Annex A
advisabletousestandard deviation insteadoftherange for the corresponding sample size.
since the later is less efficient for large samples. The
6.2.3.2 Using median method
procedure, however, is almost similar to that given
in 6.2.2.1. For each of the sub-groups, the standard From the homogenized data for dispersion
deviations shall be computed and from these values (see6.2.1.1), themedian foreachsample (M,)shallbe
the average standard deviation F shall be computed. calculated andtheaverage ofthese medians(~~ )shall
If all the individuals values are less than or equal to --i
thenbecomputed. Aquantity F2 ~ shallbecalculated
EdT (where Ed is a factor chosen from Annex A for
where the value of factor F2 is chosen from Annex A
thecorrespondingsamplesize)thentheinitialdatashall
depending uponthe sample size. Ifanyofthemedians
beconsidered tobehomogeneous. However, ifoneor
are found to lie outside the interval fi, ~ F2 R then
more s values are found to be exceeding B~I the
observations corresponding to these sub-groups shall the sub-groups corresponding to those medians shall
be discarded. For the remaining data the above be discarded. From the remaining sub-groups, afresh
procedure shall be repeated (that is, the calculation averagemedianvalueshallbecomputed andtheabove
procedure shall be repeated till all the median values
of a new average standard deviation F. and the
comparison of the remainings values with Bi F) till are found to liewithin ~, ~ Fz ~.
allthe standard deviation values are lessthan Ed F.
6.2.3.3 Using mid-range method
NOTE — LCL is notconsideredfor the homogenizationof The process of homogenization inthis case issimilar
rangesorstandarddeviationsvaluesasminimum variationin
to that for the homogenization of the medians except
theprocessisintendedandthereforeisalwayswelcome.The
onlypointtobeinvestigatedattha t stageisthecorrectnessof that the mid-range (M) has to be calculated for each
thislessvalueof rangeorstandardde viation. If sucha low sub-groups (instead of median) and the factor Fz has

valuehasreallybeenobtainedthensuchsituationsshouldbe tobereplaced by G2.The value offactor G2ischosen
institutionalizedforfuture,
from Annex A depending upon the sample size.
6,2.2.3 In the above process of homogenization, if
more than 25 percent of the sub-groups are discarded 6.3 Control Limits
for being out of control, the entire set of data maybe
6.3.1 Control Limits for Measures of Dispersion
discarded. The fresh data should be collected after
checking the process and eliminating the assignable 6.3.1.1 Range (R) chart
cause(s) which were responsible for the high rate of
The central line for the range chart is given by the
outliers inthe preliminary data.
homogenized average range value (ii ) obtained
6.2.3 Homogenization for Central Tendenqv according to 6.2.2.1. The upper control limit (UCL)
and the lower control limit (LCL) for the range chart
6.2.3.1 Using average method
areobtainedasD~ ~ andDJ ~ wherevaluesoffactors
Fromthehomogenized datafordispersion (see6.2.2.1 D~andD~areobtained fromAnnex Adepending upon
or 6.2.2.2), the average of each sub-group (X ) shall the sample size.
be calculated. The average of these averages or the
NOTE — ML fortherangechartcoincideswiththeX-axisas
D,= O.
grand average (~) for all the sub-groups shall then
be calculated. In case the data has earlier been
6.3.1.2 Standard deviation (s) chart
homogenized by using ranges (see 6.2.2.1) then a
Thecentrallineforthestandarddeviationchartisgiven
quantityA2 ~ shallbecalculated, where the factorAz
bythehomogenized average standard deviation value
ischosen fromAnnexAforthe corresponding sample
5
.. ,,