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TRAINING MATERIALON
STATISTICAL PROCESS CONTROL
(SPC)
116-A, JWALAHERI MARKET, 2nd FLOOR,PASCHIM VIHAR, NEW-DELHI-63
Ph: 011- 22!"# M$%&'(: )"10!0)))E-*+&' :'$%+'(./&(d('h&+h$$4$*
%+'+5.&hn+n%+%h$7*+&'4$*
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D(7(7&$n: A past oriented strategy that attempts to
identify unacceptable output after it has beenproduced and then separate it from the good output.
D(8(7 D(7(7&$n:Is reactionary
Tolerates wasteRelies on inspection, audits, or checks of large samplesof output
Reacts to all defects indiscriminatelyFocuses on conformance to specicationsInoles action only on outputRelies on delayed feedback for defect detectionIs not cost e!ectie
TOOLS FOR PROCESS CONTROL
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Prevention :- A future oriented strategy that improves quality and
productivity by directing analysis and action toward correcting the
process itself so that unacceptable parts will not be produced.
Defect Prevention:
Is pro-active
Avoids wasteUses small samples of product and process information
Is analytically based
Discriminates between potential defects based on causes
Involves action on the process or process parameters
Provides timely feedbacIt is cost effective
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14 M&7+5( P.$$9n :" In this techni#ue $%%& process
control is achieed by preenting all types of failures byusing modern techni#ues to get defect free product. 'erecauses are preented from making the e!ect.
(. 100 In;(7&$n: In this techni#ue $%%& checking of allthe parameters of all products has been done to get defect
free product. 'ere only defects are detected.34 S7+7&7&+' P.$( C$n7.$': In this )tatistical techni#ue
such as *ontrol *hart, 'istogram etc. are used so as toanalyses the process and achiee and maintain state ofstatistical control to get defect free product. *auses are
detected and prompting correctie action before defectoccurs.
WHY S.P.C. IS REQUIRED ? +!ectieness of any actiity inan rgani-ation is measured with respect to time and costinoled in it.
TECHNIQUES FOR PROCESS CONTROL
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Mistake Proofing 100% InspectionStatistical ProcessControl
In this method
more advancedand moderntechniques areused whichrequire substantial
investment duringits installation andmaintenance.
As it is detection type
of technique it can!tavoid failure butre"ects defectiveproducts.#equires more
inspectors$ moreinspection times andin turn more cost.
%or this technique
investment is very lessand process iscontrolled on eachworstation thereforedefective components is
not forwarded to ne&toperation. Predictabilityreduces frequentad"ustments ' in turnincreases productivity$reduces inspection cost
at station ' at finalinspection
From above we can observe that S.P.C. is the economical way of controlling
the process in comparison with Mistake Proofing and 100% inspection.
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WHAT IS S.P.C. ?14 S7+7&7& :" A alue calculated from or based uponsample data e.g. a subgroup aerage or range/ used tomake inferences about the process that produced theoutput from which the sample comes.
24 S7+7&7&+' C$n7.$' :" The condition describing a processfrom which all special causes of ariation hae beeneliminated and only common causes remain.
34 S7+7&7&+' P.$( C$n7.$' :" The use of )tatisticaltechni#ues such as control charts to analy-e a process or
it0s outputs so as to take appropriate actions to achiee andmaintain a state of statistical control and to improe theprocess capability.
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Population: A part of the universe$ which is under study for gathering
information$ is called population. (he concept would be clearer from
the following e&les:). (he number of persons out of the total employees of a company$ who
are engineers.
*. (he total number of households in a city who have computers in
house.
+. (he crop production of a particular variety in a district in the currentyear.
,. (he number of devotees visiting a shrine in a year.
any events and activities are occurring in the world
universe/. 0y maing the definition of 1population! we clearly mar the
scope of the study2 information gathering process.
It is generally neither practical nor necessary to observe the
entire population. #ather$ we observe only a small subset of it at a
time$ often doing so periodically. 3hen we do it this way$ we are said
to be sampling the population.
Populatio a! Sa"pl#
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Sample:
(o find out how the population is behaving$ we will observe only a
part of the population and gather data. 3e will then use this data to
infer something about the population. 4ample is a sub-set of thepopulation.
For example
(he number of engineers within a department$ in a company.
(he number of household in a bloc of a city$ who have computers.
(he crop production of a particular variety in a small village of thedistrict.
(he number of devotees visiting a shrine per month.
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UN$ERSTAN$ING %ARIATION
No two things are totall alike or i!entical" 5ence variation is a
natural phenomenon and is universal.
6o two products or characteristics are e&actly alie$ because any
process contains many sources of variability. (he differences among
products may be large$ or they may be almost e&tremely small$ but they
are always present.
(he diameter of a machined shaft$ for instance$ would be
affected by$ Machineclearances$ bearing wear/ #ool strength$ rate of wear/
Materialchemical composition$ hardness/ $perator part feed$ accuracy of centering/ Maintenancelubrication$ replacement of worn parts/ nvironmenttemperature$ constancy of power supply/
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4ome sources of variation in the process cause very short-run piece-to-piece
differences 7
e.g.$ baclash$ clearances within a machine and its fi&tures$
8ther sources of variation tend to cause changes in the output only over a
longer period of time$ either gradually as with tool or machine wear$ step-wise as
with procedural changes$ or irregularly$ as with environmental changes such as
power surges .
(herefore$ the time period and conditions over which measurements are
made will affect the amount of the total variation that will be present
%rom the standpoint of minimum requirements$ the issue of variation is often
simplified - parts within specification tolerances are acceptable$ parts beyond
specification tolerances are not acceptable9 reports on time are acceptable$ latereports are not acceptable. 5owever$ to manage any process and reduce
variation$ the variation must be traced bac to its sources. (he first step is to
mae the distinction between causes of variation.
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Cau& o' %aiatio
T*## a# t+o ,au& o' -aiatio&Common Causesalso called as hance auses or 6on-controllable
auses/Special Causesalso called as Assignable auses or ontrollable
auses/
C$MM$N C&'SS
Arise from causes that are inherent in the process 4ome degree affect all the output of the process ;&ist even as the process is statistically stable and behave lie a
constant system. 3hile individual measured values are different as a group they tend
to form a distribution pattern that can be described as predictable in terms of
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(he e&tent of ommon auses of variation can be indicated bysimple statistical techniques$ but the causes themselves need more
detailed analysis to isolate.
(hese common causes of variation are usually the responsibility of
management to correct$ although other people directly connected withthe operation sometimes are in a better position to identify these
causes and pass them on to management for correction.
8verall$ though$ the resolution of common causes of variation usually
requires actions on the system.
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SPCI&( C&'SS
Affect only some output of the process and are not inherent in the
process. 4pecial auses refer to any factors causing variation that cannot be
adequately e&plained by any single distribution of the process output$
as would be the case if the process were in statistical control. Unless all the special causes of variation are identified and corrected$
they will continue to affect the process output in unpredictable ways.
Examples of Sp#,ial Cau&of Variation includePeople= %atigue$ illness$ state of health.=
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Plant)Machines= #otation of machines= Differences in test or measuring devices
= 3orn out machinery or tools=
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4pecial causes of variation result in output behaviour that is usually erratic
and unpredictable.
(he discovery of a special cause of variation$ and its removal$ are usually
the responsibility of someone who is directly connected with the operation$
although management sometimes is in a better position to correct.
(he resolution of a special cause of variation$ then$ usually requires localaction. harting highlights occurrence of special causes.
4pecial auses of ?ariation= 5ave frequency distributions that are unstable over time
#esult in unpredictable outcomes= #eappear local unless action is taen
an only be eliminated by actions 1on the shop floor!
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Ra!o" %aiatio NoRa!o" %aiatio
$nl common cause are
present
Common * &ssigna+le cause
are presentCommon causes are more innos"
&ssigna+le causes are ver fewin nos"
Common causes are part ofprocess
,isitor to the process
Contri+utes to constantvariation
-ighl fluctuating variation
Pre!icta+le 'npre!icta+le
Statistics &ppl Statistics shall not appl
Management controlla+le $perating personnelcontrolla+le
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8nly a relatively small proportion of all process troubles industrial
e&perience suggests about )@/ is correctable locally by people directly
connected with the operation9 the ma"ority 7
the other B@ - is correctable only by management action on the system.
onfusion about the type of action to tae is very costly to the organiCation$
in terms of wasted effort$ delayed resolution of trouble$ and aggravated
problems. It would be wrong9 for e&le$ to tae local action e.g.$ad"usting a machine/ when management action on the system was required
e.g.$ selecting suppliers that provide consistent input materials/.
A(I864 taen to combat the above types of variation include$
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Actions on the 4ystem are those that almost always require management
action for correction and are usually required for eliminating common
causes of variation. (hese actions can correct about B@ of the process
problems.
%ARIA/LE 0 ATTRI/UTE ;very process generates data that can be categoriCed in 1?ariables
data! ' 1Attributes data!.
,aria+le !ata: ?ariables data relates to what can be measured and
e&pressed quantitatively in specific units of measurements as
dimensions$ volume$ temperature$ pressure$ time$ strength$ etc.
(he eamplesinclude: Diameter of a bearing
?olume of the cylinder (emperature of an oven 3eld strength of a location apsule filling time 5ardness of a gear
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&ttri+utes !ata: Attributes data are qualitative data where the results
are recorded in terms good or bad$ defective or defect free$ pass or fail$
yes or no$ acceptable or not acceptable$ conforming or non-conforming$
presence or absence of a desired characteristic.
!amplesinclude sticer printing acceptable or not acceptable an item meets the gauge or not Dents on body pass or fail 0raCing "oint good or bad
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SELECTING SAMPLE SI1E
8ne of the first basic questions which comes in our mind before
carrying out a survey or statistical study is 5ow many samples
should I selectEF
>enerally we select the samples as per our convenience or
without any particular logic e&cept cost ' time.
sampling is time consuming and costly$ our ob"ective in selecting a
sample is to obtain a specified amount of information about a
population at a minimum cost.
Samples ) su+groups for control charts
#ational subgroups or samples are collection of individual
measurements$ whose variation is attributable only to a constant
system of common causes. In the development ' continuing use ofcontrol charts$ subgroups or samples should be chosen in a way that
provides the ma&imum opportunity for measurements within each
subgroup to be alie sub"ect only to forces of common cause
variation/ and ma&imum chance for subgroup to differ from one
another if special cause arisebetween subgroups.
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3ithin sample or subgroup only common cause variation should be
present.
Sample si.e consi!erations
(he siCe of a rational sample is governed by the following
considerations. 4ubgroups should be sub"ect to common cause variation. 4ubgroup should ensure the presence of normal distribution for the
sample means 4ubgroups should ensure good sensitivity to the detection of special
causes. 4ubgroups should be small enough to be economically appealing
from a collection ' measurement standpoint
Generally 4 to 6 sample / subgroup is commonly used
considering the above factors.
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"ote #
4hewhart suggests / as the ideal subgroup siCe In
industrial use of control chart @ is most common ;ssential ideaof control chart is to select sub groups in such away that it gives
minimum opportunity for variation within sub group$ it is
desirable to be as small as possible for economic purpose/.
A siCe of /is better than * or + on statistical grounds9the distribution of B is nearly normal for sub groups of four or
more even though the samples are taen from non normal
universe.
4ub groups of * or + are used 86
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(his write up is for assignment any one identify Assignablecauses. As you are aware the success of any 4P program is not in ourability to collect data$ draw charts etc.$ but in effectively identifying andeliminating assignable causes. Assignable causes are those causes thatdo not allow one to predict the behavior of processes. (here is nomeaning in calculating Process apability without having a predictableprocess.
any companies have initiated 4P charts. 0ut the charts do notbenefit them. 8ne of the main reason for this is that they have notstopped the process when an assignable cause is indicated andeliminated the cause. (his is not done because no body is aware on howto do it. any e&perts only say that the cause is to be eliminated but noone is able to assist a company in doing this. 3e are sharing with you ourapproach for doing this cause elimination.
METHO$OLOG2 TO I$ENTIF2 ASSIGNA/LE CAUSES
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0efore starting the 4P data collection$ let us do the following steps:
). Identify the characteristic for which 4P is to be done.
*. 5ave a brainstorming to list all the causes that may influence the
variation in this characteristic
+. Prepare a ause ' ;ffect Diagram
,. Prepare a aster ause Analysis (able Anne&ure )/
@. Prepare a 3hy-3hy Analysis (able Anne&ure */
H. Identify factors that may affect Average and those that may affect#ange
After completion of the above$ plan for data collection$ calculationof preliminary limits$ etc. (hen use the chart for 8n -
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Sl"No Cause Is thereanSpec"
If sowhat istheSpecn"
2asis3or theSpecn
Is itchecke!* how
4hat istheactual
Diff" inSpecfn"
,s&ctual
&ctionplan
ANNE3URE 4 5MASTER CAUSE ANAL2SIS TA/LE
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Sl"No Cause 4h 4h 4h 4h 4h
ANNE3URE 4 6
WH2 4 WH2 ANAL2SIS TA/LE
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). ;nter a serial number
*. ;nter the cause from the cause and effect diagram. All the
causes from the cause and effect diagram must be covered
+. %or each cause as the uestion: Is there a 4pecificationE Please
note that the specification is for the cause. (he answer can be
Ges or 6o.
,. If there is a 4pecification$ write the actual value of the
specification. If there is no specification$ ;nter in the Action Plan
column 4pecification is to be establishedF.
@. >ive the basis for the specification mentioned in olumn 6o.,.
4ometimes the 4pecification may be based on the drawing$machine manufacturer!s catalogue$ wor instruction$ Past
;&perience$ etc. Do not write your e&pectations. 8nly enter what
is actually e&isting. #emember that there has to be some basis.
GUI$ELINES FOR USING ANNE3URE 4 5
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H. Is this specification being checed. If yes$ write the actual method used
for checing. If it is not being checed$ then enter 6o. It may be possible
that there are methods for checing but not done here$ in which case the
answer is 6o. If the answer is 6o$ then enter in the Action Plan olumnethod of checing is to be establishedF.
J. ;nter here the actual value of the cause by using the method of
checing. 4ometimes it may be the range of variation ;&: Input material
condition/ or it may be 8ne ?alue ;&: (aper in the fi&ture/. (his is the
actual value and not a guess. (ime may be required to complete thiscolumn.
B. If there is a difference between the actual value and the specification$
then e&amine how important based on technical nowledge. If the
difference is not ma"or$ then mention 6o. 8therwise mention Ges. If the
answer is Ges$ then enter in the Action Plan olumn that further analysis
is needed lie 3hy-3hy Analysis or correction to eliminate the variation.
K. Under this column enter the specific Action Plan needed as already
mentioned above.
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(his table can be used for all the causes identified in the
ause and Analysis (able with top priority for the auses found to
have variation from the aster ause Analysis (able.
). ;nter the running serial number
*. ;nter the cause to be studied
+. ;nter 3hy this cause should vary. (here may be more than one
reason. ;nter all the reasons one below the other.
,. %or each of the 3hy identified in olumn +$ write the possible
causes. 6ote that the cause is to be identified only for column +
and not bacward.
@.Proceed in the same manner as olumn ,. ;nsure that each timethe focus is only on the previous column.
H. Proceed in the same manner as olumn ,. ;nsure that each time
the focus is only on the previous column.
GUI$ELINES FOR USING ANNE3URE 4 6
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J. 1roceed in the same manner as *olumn 2. +nsure thateach time the focus is only on the preious column.
*ontinue in this manner, till any of the following happen:
a. 3o further 4hy can be answered
b. The system cause has been identied +5: 3o systemfor checking, erication, control, etc./
c. The reerse is the solution
6. 7ased on the listed why8s, deelop the action plan forimplementation.
R(*(*%(.:
. I7 & 7h( 7(*,
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SPC PROCE$URE FLOW CHARTMS&
D& C$((C#I$N
Is ProcessPre!icat+l
5I"e" In Control
N$
3in! out assigna+le
cause an! eliminateit"
6esN$
Is process No
Capa+le
Improve the
process
6es
sta+lish the Control
(imits
Prepare 7eaction
Plan
$n going
Process Control
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Measures of central ten!enc * !ispersion
(here are various measures of central tendency ' dispersion$ the most
commonly used are as follows
Mo!e: It is the most often occurring observation. It may be noted that
more than one mode may e&ist in a population.
7ange: It is the midpoint between the highest ' lowest observation.
Me!ian:It is the middle observation when all observations are arranged
in the order of magnitude.
Mean: It is arithmetic average of observations
Example: onsider a sample of )L observations as follows :
*.)$ *.@$ *.+$ *.*$ *.,$ *.,$ *.+$ *.+$ *.+$ *.)
%ind out ode$ #ange$ edian$ ean
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CONTROL CHARTS TOOL FOR SPC
Dr. 3alter 4hewhart of the 0ell
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;'ID(INS 3$7 S(C#I$N $3 &PP7$P7I C-&7#
?arious types of ontrol harts are employed based on the type of data
generated. (he chart below provides information about selection criteria of
control charts used in various situations.
< * M 7
n = 1
< * 7 o r < * s
n > 1
I s n = o r n !
, a r i a + l e
u
' n i t
c
P o r t i o n
" n i t o r # o r t io n
n = 1
n p
C o n s t a n t
p
, a r i n g
$ o n s t a n t o r % a r y i n g
n > 1
I s n = o r n !
& t t r i + u t e
# p e o f D a t a
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PROCESS CONTROL :-
A process is said to be operating instate of statistical control when the
only source of ariation is common causes.PROCESS STABILIITY: -
The process is said to be stable when the process is in control and
ariation is constant with respect to time i.e. 7eing in statistical control.
PROCESS CAPABILITY: -
The measure of inherent ariation of the process i.e )i5 )igma ;" < =/
when it is in stable condition is called as process capability.
OVER ADJUSTMENT: -
It is the practice of ad>usting each deiation from the target as if it were
due to a special cause of ariation in the process. If stable process is ad>ustedon the basis of each measurement made, then ad>ustment becomes an
additional source of ariation and inturn it increases the total ariation.
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C-C?IN; 3$7 P7$CSS P7DIC#I$N :8
Process is said to be predictable when it is in control and stable i.e. when
all 4pecial causes are removed from the process. (he process can be
checed from ontrol hart and 5istogram.
ontrol hart: - 3hen all points are within control limits or there is no
obvious run or non-random pattern of points with in the control limits.
5istogram: - 3hen bell shape is observed on 5istogram.
#;8?I6> A44I>6A0
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C&(C'(IN; P7$CSS C&P&2I(I#6: 8
After removing all special causes from the process calculate the capability
indices pand p .
If pand p is greater than ).++ then process is said to be within acceptable
capability. 0ased on the priority mae improvement plan for the process.
If pand p is less than ).++$ then find out ma"or common causes and remove
it.
S#&2(IS-IN; C$N#7$( (IMI#S: 8
3hen p and p is greater than ).++ $ (hen $ ;stablish U
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$N ;$IN; P7$CSS C$N#7$( :8
ontinuous Periodical review of control chart and recorded process
events to identify the preventive action and revise the control limits.
8P;#A(8#M4 #8#8UP.
Data Collection
Plot $n Chart
Is process in Control
I"e" no special cause
No
7efer 7eaction Plan
6es
#ake Corrective &ction
#ake Disposition
&ction 5 If 7e@!"A
&'(E )
1"&fter Corrective action taken the Imme!iate su+group shall +e measure! an! plotte!"
B"7ecor! in !etail the causes corrective action an! !isposition action taken for ever out ofcontrol con!ition"
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FACTORS FOR COMPUTING LIMITS
n !B &B D D/ B
B 1"1B 1"0 0 "BE B"EE
1"EF 1"0B 0 B"GH/ 1"HH
/ B"0GF 0"HBF 0 B"BB 1"/E
G B"BE 0"GHH 0 B"11/ 1"BF
E B"G/ 0"/ 0 B"00/ 1"1
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1" D& C$((C#I$N
8 7 C-&7#= :
87 chart is !evelope! from measurements of a particular=characteristic of a process output" 87 chart eplains process !ata in=terms of +oth its sprea! 5piece to piece varia+ilitA an! its location5process averageA"
D& C$((C#I$N:
=>Measure of (ocation
7>Measure of Sprea!
Scan the plot points confirm that the calculations an! plots arecorrect" Make sure that the plot points for the correspon!ing an! 7 is=verticall in line"
Initial stu! charts use! for first time capa+ilit or for stu!ies afterprocess improvements)changes shoul! +e the onl process control
charts allowe! on the pro!uction floor which !o not have control limitsplace! on them"
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24 CALC@LATE CONTROL LIMITS :
R ? R$ R( @@@ R / ;
B5? C$ C( @@@ C/ ; 4here
is the number of subgroups.
R$is the range of the rst subgroup.
=5 is the aerage of the rst subgroup.
S(7; $n7.$' h+.7 :
= and R charts are normally drawn with the= chart aboe the Rchart.
Data block should include spare for each indiidual reading, aerage= /, Range R / and the date;time or other identication of thesubgroup.
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*haracteristics to be plotted are the sample aerage = / andthe sample si-e R / for each subgroup, collectiely these reEect
the oerall process aerage and its ariability.Aerage =/ ? C$ C( @@@. Rn / ; n
4here n subgroup sample si-e.
Range R / ? 'ighest Gowest
S('(7 7h( S+'( 8$. $n7.$' h+.7 :)ome general guidelines for determining the scales may be
helpful, although they may hae to be modied in particularcircumstances.
F$. = Ch+.7 :The di!erence between the highest and the
lowest alues on the scale should be at least two times thedi!erence between the highest and the lowest of the subgroupaerages =/.
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F$. R Ch+.7 :
Halue e5tends from -ero to an upper alue about two times the largest range.
F$. R Ch+.7 :
*GR? D2RJJ
G*GR ? D< RJJ
F$. B Ch+.7 :
*G5 ? CK A( RJJ
G*G5 ? CK " A( RJJ
4here D2, D
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3. INTERPRETATION FOR PROCESS CONTROL
)ince the ability to interpret either the subgroup ranges or
subgroup aerages depends on the estimate of piece to pieceariability, the R chart is analy-ed rst. The data points arecompared with the control limits, for points out of control or forunusual patterns or trends.
For Range *hart :
a/ 1oints beyond the control limits are primary eidence of non"control of that point. Any point beyond a control limit is the signalfor immediate analysis of the operation for the special cause.
A point aboe the control limit is generally due to
$/ 1lot point may be miscalculated.
(/ 1iece to piece ariations has increased.
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A point below the control limit is generally due to
$/ 1lot point is in error.
(/ 1iece to piece ariation has decreased.
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%ind and Address 4pecial auses
%or each indication of special cause in the range data$ conduct an
analysis of the operation of the process to determine the cause and toimprove the process.
A process log may also be a helpful source of information in terms of
identifying special causes of variation. 4ingle point out of control is reason to
begin an immediate analysis of the process.
#ecalculate ontrol
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4
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AnalyCe the data on the A?;#A>; 5A#(
3hen the ranges are in statistical control$ the process spread 7 the
within subgroup variation is considered to be stable. (he averages canthen be analyCed to see if the process location is changing over time.
ontrol limits for &O
are based upon the variation in the ranges. (hen ifxxxxxxxxxxx
the averages are in statistical control$ their variation is related to the
amount of variation seen in the ranges common cause variation of the
system/. If the averages are not in control$ some special causes ofvariation are maing the process location unstable.
Points beyond control limits indicates that there is
)/ shift in process
*/ Plot points are in error.
%ind and address the special causes and then recalculate the control
limits after eliminating the special causes.
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#4 INTERPRET FOR PROCESS CAPAILIT
Interpretation process capability is to be carried out only under thefollowing assumptions:
$/ 1rocess is statistically stable.
(/ Indiidual measurements from the process conform to normaldistribution.
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*alculate 1rocess )tandard Deiation:
)ince within subgroup process ariability is reEected in thesubgroup aerages, the estimate of the process standard
deiation N=N can be based on the aerage range R/. =? RJ ; d(
4here
RJ the aerage of the subgroup ranges.
d(the constant arying by sample si-e.*apability can be described in terms of the distance of the
process aerage from the specication limits in standarddeiation units, O.
For unilateral tolerance
O ? )G CK/ ; = or/ O ? 5K "G)G / ; =
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%or bilateral tolerance
U4