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Training Material on SPC

GLOBAL SERVICESCONSULTANCY ON TOTAL QUALITY MANAGEMENT

TRAINING MATERIAL

ON

STATISTICAL PROCESS CONTROL

(SPC)

116-A, JAWALAHERI MARKET, 2nd FLOOR, PASCHIM VIHAR, NEW-DELHI-63Ph: 011 - 3012161

M!"#$%: &10'0(, &1&(3623E-)*#$ : +$!"*$%.#/%d%$h#*h!!/!)

"*$*4#hn*n"*"5%d#)*#$/!)

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mailto:[email protected]:[email protected]


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TOOLS FOR PROCESS CONTROL

1. Detection :- A past oriented strategy that attempts to identify unacceptable output

after it has been produced and then separate it from the good output.2. 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.

TECHNIQUES FOR PROCESS CONTROL

1. Mistae Proo!in" :-In this technique 100% process control is achieved by preventing

all types of failures by using modern techniques to get defect free product. ere causes

are prevented from ma!ing the effect.

2. #$$% Ins&ection : In this technique 100% chec!ing of all the parameters of all

products has been done to get defect free product. ere only defects are detected.

3. Statistica' Process Contro' : In this "tatistical technique such as #ontrol #hart$

istogram etc. are used so as to analyses the process and achieve and maintain state of

statistical control to get defect free product. #auses are detected and prompting #A

before defect occurs.

(H) S*P*C* IS REQUIRED +

ffectiveness of any activity in an &rgani'ation is measured with respect to time and cost

involved in it.

Mistae Proo!in" #$$% Ins&ection Statistica' Process Contro'

In this method more

advanced and modern

techniques are used

which require

substantial investment

during its installation

As it is detection type of

technique it can(t avoid

failure but re)ects

defective products.

*equires more inspectors$

more inspection times and

+or this technique investment is

very less and process is controlled

on each wor!station therefore

defective components is not

forwarded to ne,t operation.

-redictability reduces frequent



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and maintenance. in turn more cost. ad)ustments in turn increases

productivity$ reduces inspection

cost at station at final inspection

+rom above we can observe that ".-.#. is the economical way of controlling the processin comparison with /ista!e -roofing and 100% inspection.

(HAT IS S*P*C* +

1. Statistics :- A value calculated from or based upon sample data e.g. a subgroup

average or range used to ma!e inferences about the process that produced the output

from which the sample comes.

2. Statistica' Contro' :- he condition describing a process from which all special

causes of variation have been eliminated and only common causes remain.

3. Statistica' Process Contro' :- he use of "tatistical techniques such as control charts

to analy'e a process or it(s outputs so as to ta!e appropriate actions to achieve and

maintain a state of statistical control and to improve the process capability.

STATISTICAL PROCESS CONTROL

,ARIATION: -he inevitable differences among individual outputs of a process3 the

sources of variation can be grouped into two ma)or classes4 #ommon #auses and "pecial

#auses.

Coon Ca.ses: -A source of variation that affect all the individual values of the

process output and inherent in the process itself and can not be eliminated totally.

S&ecia' Ca.ses: -A source of variation that is intermittent$ unpredictable$ unstable3 his

causes can be identifiable and can be eliminated permanently.

Ran/o ,ariation Non-Ran/o ,ariation &nly common cause are present #ommon Assignable cause are

present

#ommon causes are more in nos. Assignable causes are very few in nos.

#ommon causes are part of process 5isitor to the process

#ontributes to constant variation ighly fluctuating variation



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-redictable 7npredictable

"tatistics Apply "tatistics shall not apply

/anagement controllable &perating personnel controllable

PROCESS CONTROL :-

A process is said to be operating instate of statistical control when the only source of

variation is common causes.

PROCESS STA0ILIIT): -

he process is said to be stable when the process is in control and variation is constantwith respect to time i.e. 8eing in statistical control.

PROCESS CAPA0ILIT): -

he measure of inherent variation of the process i.e "i, "igma :; 6


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effectively identifying and eliminating assignable causes. Assignable causes are those

causes that do not allow one to predict the behaviour of processes. here is no meaning in

calculating -rocess #apability without having a predictable process.

/any companies have initiated "-# charts. 8ut the charts do not benefit them* One o!

t2e ain reasons !or t2is is t2at t2e3 2ave not sto&&e/ t2e &rocess 42en an

assi"na5'e ca.se is in/icate/ an/ e'iinate/ t2e ca.se* his is not done because no

body is aware on how to do it. /any e,perts only say that the cause is to be eliminated

but no one is able to assist a company in doing this. >e are sharing with you our

approach for doing this cause elimination.

8efore starting the "-# data collection$ let us do the following steps4

1. Identify the characteristic for which "-# is to be done.

2. ave a brainstorming to list all the causes that may influence the variation in this

characteristic

6. -repare a #ause ffect ?iagram

=. -repare a /aster #ause Analysis able Anne,ure 1

@. -repare a >hy;>hy Analysis able Anne,ure 2

. Identify factors that may affect Average and those that may affect *ange

After completion of the above$ plan for data collection$ calculation of preliminary limits$

etc. hen use the chart for &n ;Bine control.

>hen you are routinely using the chart$ when ever a point goes beyond the control limits$

using the /aster #ause Analysis able$ we can narrow the assignable cause 8ased on our

preliminary listing as mentioned in "l. Co. above by verifying the condition of the cause

from the limits specified in the table.

ANNEXURE 1MASTER CAUSE ANAL)SIS TA0LE

S'*

No*

Ca.se Is t2ere a

s&ecn+

I! so6 42at

is t2e

s&ecn+

0asis !or

t2e s&ecn*

Is it

c2ece/

an/ 2o4+

(2at is

t2e

act.a'+

Di!!* in

S&ec!n*

,s

A

&

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Act.a'

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ANNEXURE 2

(H) 7 (H) ANAL)SIS TA0LE

S'*

No*

Ca.se (H) (H) (H) (H) (H)

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GUIDELINES FOR USING ANNE8URE 7 #

1. nter a serial number

2. nter the cause from the cause and effect diagram. All the causes from the cause and

effect diagram must be covered

6. +or each cause as! the Euestion4 Is there a "pecificationF -lease note that the

specification is for the cause. he answer can be Ges or Co.

=. If there is a "pecification$ write the actual value of the specification. If there is no

specification$ nter in the Action -lan column H"pecification is to be established.

@. Jive the basis for the specification mentioned in #olumn Co.=. "ometimes the

"pecification may be based on the drawing$ machine manufacturer(s catalogue$ wor!

instruction$ -ast ,perience$ etc. ?o not write your e,pectations. &nly enter what is

actually e,isting. *emember that there has to be some basis.

. Is this specification being chec!ed. If yes$ write the actual method used for chec!ing.

If it is not being chec!ed$ then enter Co. It may be possible that there are methods for

chec!ing but not done here$ in which case the answer is Co. If the answer is Co$ then

enter in the Action -lan #olumn H/ethod of chec!ing is to be established.

D. nter here the actual value of the cause by using the method of chec!ing. "ometimes

it may be the range of variation ,4 Input material condition or it may be &ne 5alue

,4 aper in the fi,ture. his is the actual value and not a guess. ime may be

required to complete this column.

K. 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$ thenmention Co. &therwise mention Ges. If the answer is Ges$ then enter in the Action

-lan #olumn that further analysis is needed li!e >hy;>hy Analysis or correction to

eliminate the variation.

9. 7nder this column enter the specific Action -lan needed as already mentioned above.

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GUIDELINES FOR USING ANNE8URE 7 9

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.

1. nter the running serial number

2. nter the cause to be studied

6. nter >hy this cause should vary. here may be more than one reason. nter all the

reasons one below the other.

=. +or each of the >hy identified in #olumn 6$ write the possible causes. Cote that the

cause is to be identified only for column 6 and not bac!ward.

@. -roceed in the same manner as #olumn =. nsure that each time the focus is only on

the previous column.

. -roceed in the same manner as #olumn =. nsure that each time the focus is only on

the previous column.

D. -roceed in the same manner as #olumn =. nsure that each time the focus is only onthe previous column.

#ontinue in this manner$ till any of the following happen4

a. Co further >hy can be answered

b. he system cause has been identified ,4 Co system for chec!ing$ verification$

control$ etc.

c. he reverse is the solution

8ased on the listed whyLs$ develop the action plan for implementation.

*emember4

It is the system$ which is at the *oot #ause of all problems and not individuals.



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SPC PROCEDURE FLO( CHART

/"A

?AA #&BB#I&C

Is process Co +ind out

-redictableF Assignable causes i.e. In #ontrol and eliminate it.

Ges

Is process Co

#apableF Improve the process

Ges

stablish the#ontrol Bimits

-repare *eaction -lan

&n going -rocess #ontrol



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PREDICTA0LE PROCESS :- -rocess free from Assignable causes*

CAPA0ILIT) :- /easure of inherent variation*

#A-A8B -*"" 4 #p #p! M 1.66

#*MEASUREMENT S)STEM ANAL)SIS :

/easurement "ystem Analysis measures the contamination of the variation due to

measurement system in the total variation of characteristic. In this technique both variable

and attribute data measurement systems are verified.

+ollowing types of variations are observed in /.".A.

1. quipment 5ariation 4; 5ariation of measuring instrument.

2. Appraiser 5ariation 4; 5ariation between measuring persons.

3. #ombine 5ariation 4; 5ariation of both instruments and person.

4. -art to -art 5ariation 4; 5ariation comes when measuring two different parts.

5. >ithin -art 5ariation 4; 5ariation comes when measuring same part at different

places.

*esultant of all these variation is called as otal 5ariation in the measuring system.

*eproducing and *epeatability "tudy are conducted to evaluate quipment 5ariation and

Appraiser 5ariation.

his * * value should be less than 10% when it is between 10 to 60%$ then measuring

system requires improvement. 8ut if this variation is more than 60% then measurement

system required to be changed.

9* DATA COLLECTION :-

?ata is available in two types 4

1. 5ariable data 4 ?ata which is available in numerical form.

2. Attribute ?ata 4; ?ata which is in term of decision and not in numerical terms. e.g. ;

?ata form Jo;Co go gauges.



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* CHEC;ING FOR PROCESS PREDICTION :-

-rocess is said to be predictable when it is in control and stable i.e. when all "pecial

causes are removed from the process. he process can be chec!ed from #ontrol #hart and

istogram*

Contro' C2art: ->hen all points are within control limits or there is no obvious run or

non;random pattern of points with in the control limits.

Histo"ra: ->hen bell shape is observed on istogram.

REMO,ING ASSIGNA0LE CAUSES:

>hen process is fail to satisfy above requirements then e,istence of special causes may be

there. In this cause find special causes and remove.

hen #p and #p! is greater than 1.66 $ hen $ stablish 7#B:B#B and #B mar!ed on

control chart and Issued to &perators for ongoing control.

>* PREPARE REACTION PLAN: -

After deciding control limits$ #orrective and disposition actions to be given to the

operators for any special causes e,pected to occur during the process. hese corrective

and disposition actions can be documented in *eaction -lan.



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?* ON GOING PROCESS CONTROL :-

#ontinuous -eriodical review of control chart and recorded process events to identify the

preventive action and revise the control limits.

OPERATOR@S ROLE IN SPC FOR INDI,IDUAL SU0-GROUP*

?ata #ollection

-lot &n #hart

Ges

Is process in #ontrol F

i.e. no special cause

Co

*efer *eaction

-lan

a!e #orrective

Action

a!e ?isposition Action If *eqd.

NOTE :

#*A!ter Corrective action taen6 t2e Ie/iate s.5"ro.& s2a'' 5e eas.re/ an/

&'otte/*

9*Recor/ in /etai' t2e ca.ses6 corrective action an/ /is&osition action taen !or ever3

o.t o! contro' con/ition*



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FACTORS FOR COMPUTING LIMITS

n /9 A9 D D< E9

9 #*#9 #*$ $ *9> 9*>>

#*>B #*$9 $ 9*=?< #*??

< 9*$=B $*?9B $ 9*99 #*= 9*9> $*=?? $ 9*##< #*9B

> 9*=< $*


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It is a technique$ which builds quality into the process. "-# is most effective when

problems are resolved as soon as identified. #ontrol charts are mainly to increase

productivity$ improve quality and reduce cost. -rocess variation can be easily analysed by

control charts. &b)ective of control chart analysis is to identify any evidence that through

process variability or the process averages are not operating at a constant level.

he goal of the process control chart is not perfection$ but a reasonable and

economical state of control.

CONTROL CHARTSFOR ,ARIA0LES

N 8A* * chart is developed from measurements of a particular characteristic of a process

output. his chart is pertaining to variables. #ontrol charts for variables are powerful tools

that can be used when measurements from a process are available.

>ith variable data performance of a process can be analysed and improvement can be

qualified even if all individual values are within the specification limits.

8asically fewer pieces need to be chec!ed before ma!ing reliable decisions. "o the time

gap between production of parts and corrective action often cab be shortened.

#* DATA COLLECTION

8 5ar -R CHART:

N bar ;* chart is developed from measurements of a particular characteristic of a

process output. N bar;* chart e,plains process data in terms of both its spread piece to

piece variability and its location process average.

?AA #&BB#I&C4

N/easure of Bocation

*/easure of "pread

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o analy'e the particular characteristics of a process or process output$ data are

collected in small subgroups of constant si'e 2 to @ consecutive pieces. "ubgroups are

ta!en periodically. "ample si'e should remain constant for all subgroups.

"78J*&7- "IO4

"ubgroup si'e should be chosen so that opportunities for variation among the units

within a subgroup are small. If the variation within the subgroup represents the piece to

piece variability over a very short period of time$ then any unusual variation between

subgroups would reflect changes in process that should be investigated for appropriate

action.

-ieces within each subgroup would all be produced under very similar production

condition over a very short time. "o the variation within each subgroup would primarily

reflect common causes.

"78J*&7- +*E7C#G4

-urpose of selecting subgroup is to detect changes in the process over time.

?uring an initial process study$ the subgroups are often ta!en consecutively or at

short intervals$ to detect whether the process can shift to show other instability over brief

time periods. As the process demonstrates stability$ the frequency of subgroups can be

increased.

C7/8* &+ "78J*&7-"4

+rom a process standpoint$ enough subgroups should be gathered to assure that the

ma)or sources of variation have had an opportunity to appear. Jenerally 2@ or more

subgroups containing 100 or more individual readings give a good test for stability.

-lot the averages and *anges on the #ontrol #harts4

-lot the averages and ranges on their respective charts. his should be done as

soon as possible after scaling has been decided. #onnect the points with lines to help

visuali'e patterns and trends.



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"can the plot points$ confirm that the calculations and plots are correct. /a!e sure

that the plot points for the corresponding N and * is vertically in line.

Initial study charts used for first time capability or for studies after process

improvements:changes should be the only process control charts allowed on the

production floor which do not have control limits placed on them.

9* CALCULATE CONTROL LIMITS :

* P *1 *2 QQQ *R : R

N P N1 N2 QQQ NR : R

>here

R is the number of subgroups.

*1is the range of the first subgroup.

N1is the average of the first subgroup.

"etup control charts 4

N and * charts are normally drawn with the N chart above the * chart$ and a data

bloc!. he values of N and * will be the vertical scales.

?ata bloc! should include spare for each individual reading$ average N $ *ange

* and the date:time or other identification of the subgroup.

#haracteristics to be plotted are the sample average N and the sample si'e *

for each subgroup$ collectively these reflect the overall process average and its variability.

Average N P N1 N2 QQQ. *n : n

>here nsubgroup sample si'e.

*ange * P ighestS Bowest

"elect the "cales for control charts 4

"ome general guidelines for determining the scales may be helpful$ although they

may have to be modified in particular circumstances.

+or N #hart 4

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he difference between the highest and the lowest values on the scale

should be atleast two times the difference between the highest and the lowest of the

subgroup averages

N .

+or * #hart 4

5alue e,tends from 'ero to an upper value about two times the largest

range.

+or * #hart 4

7#B*P ?= *

B#B* P ?6 *

+or N #hart 4

7#B, P N A2 *

B#B, P N ; A2 *

>here ?=$ ?6$ A2 are constants varying by sample si'e with values from sample si'es from

2 to 10.

?raw the average * and process average N as solid hori'ontal lines.

#ontrol limits 7#B* $ B#B*$7#B,$ B#B, as dashed hori'ontal lines. Babel the lines.

*INTERPRETATION FOR PROCESS CONTROL

"ince the ability to interpret either the subgroup ranges or subgroup

averages depends on the estimate of piece to piece variability$ the * chart is analysed first.

he data points are compared with the control limits$ for points out of control or for

unusual patterns or trends.

+or *ange #hart 4

a -oints beyond the control limits are primary evidence of non;control of that

point. Any point beyond a control limit is the signal for immediate analysis of the

operation for the special cause.

A point above the control limit is generally due to

1 -lot point may be miscalculated.

2 -iece to piece variations has increased.

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6 /easurement system has changed.

A point below the control limit is generally due to

1 -lot point is in error.

2 -iece to piece variation has decreased.

6 /easurement system has changed.

b -resence of unusual patterns or trends even when all ranges are within control

limits$ can be evidence of change of process spread$ also indicates some special causes.

c *uns

1 D points in a row on one side of the average indicate that the process is

not normally distributed and there is shift in the process average.

2 D points in a row that are consistently increasing or decreasing.

d -resence of cycles in the chart indicates that special causes due to machine set

up$ non;uniformity in the material wear of machine.

Fin/ an/ A//ress S&ecia' Ca.ses

+or each indication of special cause in the range data$ conduct an analysis of the

operation of the process to determine the cause and to improve the process.

A process log may also be a helpful source of information in terms of identifying

special causes of variation. "ingle point out of control is reason to begin an immediate

analysis of the process.

Reca'c.'ate Contro' Liits

>hen conducting an initial process study or a reassessment of process capability$

the control limits should be recalculated to e,clude the effects of control periods for which

process causes have been clearly identified and removed.



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Analy'e the data on the A5*AJ #A*

>hen the ranges are in statistical control$ the process spread S the within subgroup

variation is considered to be stable. he averages can then be analysed to see if the process

location is changing over time.

#ontrol limits for N 8ar are based upon the variation in the ranges. hen if 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 of variation are ma!ing the process location unstable.

-oints beyond control limits indicates that there is

1 shift in process

2 -lot 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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Ca'c.'ate Process Stan/ar/ Deviation4

"ince within subgroup process variability is reflected in the subgroup averages$ the

estimate of the process standard deviation H


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Eva'.ate &rocess ca&a5i'it3

It is necessary to evaluate the process capability in terms of meeting customer

requirements.

+undamental goal is never ending improvement in process performance.

Improve the process performance by reducing the variation that comes from

common causes$ or shift the process average close to the target. his generally means

ta!ing management action to improve the system.

I&rove Process Ca&a5i'it3

o improve process capability$ there must be increased attention on reducing the

common causes. Accounts must be directed towards the system namely$ the underlying

process factors which account for the process variability such as1 /achine performance.

2 #onsistency of input materials.

6 8asic methods by which process operates.

= raining methods.

@ >or!ing environment.

As a general rule these system;related causes for unacceptable process capability may be

beyond the abilities of the operator or their local supervisor to correct. Instead they may

require management intervention to ma!e basic changes$ allocate resources and provide

the co ordination needed to improve the overall process performance.

8 7 S Avera"e an/ Stan/ar/ Deviation c2arts

*ange charts were developed as measures of process variation because the range is

easy to calculate and is relatively efficient for small subgroup sample si'es. "ample

standard deviation H " H is more efficient indicator of process variability especially with

larger sample si'es. It is sensitive in detecting special causes of variation.

Gat2er Data

1 If raw data are voluminous$ they are often recorded on a separate data sheet.

2 calculate subgroup sample standard deviation

" P V NIS N 2: n S 1 W1:2

>here NIIndividual values



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NAverage

n"ample si'e.

Cote4 ?o not round off N values.

Ca'c.'ate Contro' Liits

7#B"P 8="

B#B"P 86"

7#BNP N A6"

B#BNP N ; A6"

>here

"Average of individual subgroup samples standard deviation.

8=$ 86$ A6#onstants varying by sample si'es.

Inter&ret !or Process Contro'

*efer N S * chart(s Interpretations for process control.

Inter&ret !or Process Ca&a5i'it3

*efer N S * chart(s Interpretations for process capability.

-rocess "tandard deviation$

& P " : #=

where

"Average of sample standard deviation.

#=#onstant varying by sample si'e.

MEDIAN CHARTS

/edian charts are alternatives to N and * charts for control of processes with

measured data.

1 easy to use



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2 "ince a single chart shows both the median and spread$ it can be used to

compare the output of several processes.

Gat2er /ata

1 /edian charts are used with subgroup sample si'e of 10 or less. &dd sample

si'es are more convinient.

2 If using even si'e subgroups$ the median is the average of middle two units.

6 nter the subgroups median N and range * in the table. It is

recommended to also plot the range chart to observe trends or runs in range.

Contro' Liits

7#B*P ?=*

B#B*P ?6*

7#BNP N A2*

B#BNP N ; A2*

where

?=$?6$A2are constants varying by sample si'es.

Interpret for process control and process capability is same as that of N S * charts refer

bac! .

CHARTS FOR INDI,IDUAL AND MO,ING RANGE 8 - MR

It is necessary for process control to be based on individual readings rather than

subgroups. #ontrol chart for individuals can be constructed as described below.

In such cases the within subgroup variation is effectively 'ero.

1 #harts for individuals are not sensitive in detecting process changes as N and *

charts.

2 "ince there is only one individual item per subgroup$ values of N and & can

have substantial variability even though the ptocess is stable untill the

number of subgroups is 100 or more.

Gat2er Data

1 Individual readings N are recorded.

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2 #alculate the moving range /* between the individuals. It is generally best

to record the difference between each successive pair of readings eg4

difference between first and second reading $ the second and third etc..

6 here will be one less such moving range than there are individual readings.

Contro' Liits

7#B/*P ?=*

B#B/*P ?6*

7#BNP N 2*

B#BNP N ; 2*

where

* is the average moving range.

N is the process average.

?=$ ?6and 2are constantsthat vary according to the sample si'e n.

Interpret for process control and process capability is same as that of N S * chart refer

bac!.

P CHART

- chart measures the proportion of non conforming items in a group of items being

inspected.

eg4 D pieces are defective out of D0 pieces.

8efore - chart can be used several preparatory steps must be ta!en 4

1 stablish an environment suitable for action.

2 -rocess must be understood in terms of its relationship to other

operations:users and in terms of the process elements

people$equipment$material$methods$environment. echnique such as cause

and effect diagram help ma!e these relationships visible.

S.5"ro.& Sie4

#harts for attributes require large subgroup si'es to be able to detect moderate shift

in performance.

eg4 n- M @

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S.5"ro.& Fre.enc34

"ubgroup frequency should ma!e sense in terms of production periods.

short time intervals allow faster feedbac!.

S.5"ro.& N.5er4

It must vbe large enough to capture all the li!ely sources of variation affecting the

process. Jenerally 2@ or more subgroups.

Pro&ortion Non Con!orin"4

Cumber of items inspectedn

Cumber of non conforming items foundn-

-roportion Con #onforming$ - P n- : n-rocess Average -roportion Con #onforming$

- P n1-1 n2-2 QQQQQQ. nR-R : n1 n1 QQQ.. n1

Contro' Liits4

7#B-P - 6 V - 1 S - : nW1:2

B#B-P - ; 6 V - 1 S - : nW1:2

where n is the constant sample si'e.

"uppose if the sample si'e varies then ta!e average of sample si'e n .

hen

7#B-P - 6 V - 1 S - : nW1:2

B#B-P - ; 6 V - 1 S - : nW1:2

Inter&ret !or Process Contro'4

-oints above upper and lower control limit is generally sign of higher proportion

non conforming.

Average number of non conforming items per subgroup n- is large 9 or more$

the distribution of the subgroup is nearly normal and trend analysis can be used. >hen n-

becomes small$ trend and run analysis is not applicable.



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Inter&ret For Process Ca&a5i'it34

+or a - chart$ process capability is reflected by the process average non

conforming p.

eg4 If - P 0.0612

-rocess capability currently is 6.12% failures of the functional chec! 9.KK% o!.

Eva'.ate t2e Process Ca&a5i'it34

-rocess capability as )ust calculated reflects the ongoing level of performance that

the process of generating and can be e,pected to generate as long as it remains in control.

nP CHART

n- chart measures the number of non conforming items in an inspection. It proves

the actual numberof non conforming items rather than proportion of the sample.

Gat2er Data4

"ample si'es must be equal.

"amples should large enough to allow several non conformingitems to appear in

each subgroup.

Contro' Liits4

-rocess Average Con #onforming is n-

7#Bn-P n- 6 Vn- 1;-W1:2

B#Bn-P n- ; 6 Vn- 1;-W1:2

Process Ca&a5i'it34

Cote that the process capability for an n- chart is still -.

C 7 CHART

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#;#hart is used when number of defects are found in single unit or product.

Data Co''ection4

"ample si'e must be constant. It is applied to

1 Con conformities are scattered through a continous flow of product.

eg4 flaws in a bolt of vinyl$ bubbles in glam.

Ca'c.'ate Contro' Liits4

-rocess average number of non conformities

# P #1 #2 QQQ #R : R

7#B#P # 6 # 1:2

B#B#P # ; 6 # 1:2

Process Ca&a5i'it34

-rocess #apability is #.

U CHART

7 S #hart measures the number of non conformities per inspection reporting unit

in subgroups which can have varying sample si'es.

It is similar to #;#hart e,cept that the number of non conformities is e,pressed on

a per unit basis.

Contro' Liits4

7 P # : n

where #number of non conformities found.

nsample si'e of the subgroup.

#alculate process average non conformities 7 .

7#B7P 7 6 7 : n1:2

B#B7P 7 ; 6 7 : n1:2

-rocess capability is 7$ the average number of non conformities per reporting unit.

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