PPT 13 Process Capability

7/25/2019 PPT 13 Process Capability

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Statistical Process Control

Session 13

Control Charts and ProcessCapability


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Statistical Process Control (SPC)

Every output measure has a target value and a level ofacceptable variation (upper and lower tolerance limits)

SPC uses samples from output measures to estimate the

mean and the variation (standard deviation)

Example

e want water bottles to be filled with 12 FL OZ 0.05 FL OZ

!uestion"

#ow do we define the output measures$


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hen should we useX/Rcharts$

%& 't is not possible to label good or bad

& 'f we have relatively smaller sample sies (*+)

Statistical Process Control with X/RCharts


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,a-e t samples of sie n (sample sie should be . or more)

=

=n

i

ix

nX

%

%

/0min/0maxii

xxR =

Ris the range between the highest and the lowest for each sample


X is the mean for each sample


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=

=t

j

jXt

X%

%

=

=t

j

jR

t

R

%

%


Xis the average of the averages&

Ris the average of the ranges


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RAXLCL

RAXUCL

X

X

(

(

=

+=

define the upper and lower control limits1

RDLCL

RDUCL

R

R

2

3

=

=


4ead 56 726 73from

,able


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Example" SPC for bottle filling1

Sample Observation (xi) Average Range

(R)

% %%&8+ %%&8 12.09 %%&8% %&+%

%&+2 %&+2 11.92 %%&89 %&+9

2 %%&8 %&+ 11.93 %&+% %&+9

3 %%&8: %&+: 12.00 %%&8% %%&8;

. %%&8. %&%+ 12.03 %&+9 %&++

: %%&88 %%&8; 11.94 %&+: %&+:

9 %&++ %&+3 11.92 %&++ %&+9

; %&+ %&+: 11.94 %&+9 %&++

8 %&+% %&+: 11.94 %%&8% %%&83


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Example" SPC for bottle filling1

Sample Observation (xi) Average Range

(R)

% %%&8+ %%&8 12.09 %%&8% %&+% %%&89 +&%8

%&+2 %&+2 11.92 %%&89 %&+9 %&++ +&%.

2 %%&8 %&+ 11.93 %&+% %&+9 %%&88 +&%.

3 %%&8: %&+: 12.00 %%&8% %%&8; %%&8; +&%.

. %%&8. %&%+ 12.03 %&+9 %&++ %&+2 +&%.

: %%&88 %%&8; 11.94 %&+: %&+: %&+% +&%

9 %&++ %&+3 11.92 %&++ %&+9 %&+% +&%.

; %&+ %&+: 11.94 %&+9 %&++ %&+ +&%2

8 %&+% %&+: 11.94 %%&8% %%&83 %%&89 +&%.

%+ %%&8 %&+. 11.92 %&+8 %&+9 %&+% +&%9

Calculate the average and the range for each sample1


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,hen1

++&%(=X

is the averageof the averages

%.&+=R

is the averageof the ranges


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=C= > %%&8+

?C= > %&%+

,he @ Chart

@ > %&++


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,he 4 Chart

=C= > +&++

4 > +&%.

?C= > +&2


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,he @A4 Chart

=C=

?C=

@

=C=

4

?C=

hat can youconclude$


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Process Capability


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Process Capability

It is the number of times the spreadof the process ts into the tolerancewidth.

The higher the value of Cp the better

the process

if Cp

! ".# the spread of the process

ts "$ times into the tolerancewidth while Cp ! 1 means that thespread is e%ual to the tolerance

width.


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Process Capability Inde&

Cp'denes the position of the process in relation to the

tolerance limits

It is not much use having a high Cp inde& if the processsetting is way o( centre in relation to the middle of the

tolerance range. ) high Cp'inde& means then that you have a good

process with a small spread in relation to the tolerancewidth and also that it is well centred within that width.

If Cp'is e%ual to Cp the process is set to produce e&actly in

the middle of the tolerance range *see +ig. ,-. ) normal re%uirement is that Cp' should be at least 1.33.

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PPT 13 Process Capability