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Statistical Process Control
INTRODUCTION
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Statistical Process Control
What is SPC ?
What is VSC ?
Why we use control charts ?
Plotting of control chart ...
Statistical Process Control
The Arithmetic mean :
Most of the time when we refer to the average of something we
are talking about arithmetic mean only. To find out the
arithmetic mean , we sum the values and divide by the number
of observation.
Advantages : it's a good measure of central tendency.It easily
understood by most people
Disadvantages :- Although the mean is reliable in that it reflects
all the values in the data set, it may also be affected by extreme
values that are not representative of the rest of the data.
Statistical Process Control
The Median :
The median is a single value from the data set that measures the
central item in the set of numbers.Half of the item lie above this
point and the other half lie below it.
We can find median even when our data are qualitative
descriptions.
For example we have five runs of the printing press the results
of which must be rated according to the sharpness of the image.
Extremely sharp, very sharp, sharp slightly blurred, and very
blurred.
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Mode :The mode is a value that is repeated most often in the data set.
Infect it is the value with highest frequency.
Statistical Process Control
Average Income
Country X
10,000 Rs/Month
Country Y
11000 Rs/Month
Which country is ECONOMICALLY more stable ???
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Country X
Avg.
Std dev.
Country Y
8000
12000
10000
9000
11000
46000
3000
1000
3000
2000
10000
11000
1414
17516
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Standard Deviation is the
Measure
of
SPREAD
sigma
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
(sigma)
√
=
_
_ 2
_
2
2
(x-x1 ) + (x-x2) + … (x-x )
n
(n - 1)
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Plot HISTOGRAM for following DATA
4.2
5.2
5.4
2.1
9
9.6
13
14
15
9.6
Data
12.4
14.8
18
17
19
15.5
2
5
7
10.1
6
7.8
11
11.8
9.4
10.8
10
11
10.1
8.8
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Normal Distribution Curve
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Properties of a normal model curve :-
•It is symmetrical , unimodel and bell shaped.
•The values of mean , median and mode are identical.
•It is uniquely determined by the two parameters , namely mean
and standard deviation.
•In the family of normal curves smaller the standard deviation ,
higher will be the peak.
•If the original observations follow a normal model with mean mu
and std dev sigma then the averages of random sample of size n
drawn from this distribution will also follow a normal distribution.
The mean of the new model is same as the original model I.e mu
but the standard deviation gets reduced to  (sigma)/root "n"
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99.73%
+/-3 sigma
95.45%
+/- 2 sigma
68.26%
+/- 1 sigma
2.14% 13.6%
34.13% 34.13%
13.6%
2.14%
Statistical Process Control
Description of a
NORMAL DISTRIBUTION
LOCATION:
L
O
C
A
T
I
O
N
The central tendency
it is usually expressed as the
AVERAGE
SPREAD:
The dispersion
it is usually expressed as SIGMA
S
P
R
E
A
D
Statistical Process Control
A Process Control System
•THE PROCESS
•INFORMATION ABOUT PROCESS
•ACTION ON THE PROCESS
•Local Action - Special cause
•Action on the System - Common cause
•ACTION ON THE OUTPUT
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DEMING’s Funnel Experiment
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Variation :- Common cause and Special Cause
In order to effectively use of process control measurement data, it is important to understand the concept of
variation.
No two characteristic or products are exactly alike, because any process contain many source of variability.
Some source of variation in the process cause short-term, piece to piece difference's - e.g., backlash and
clearance with in a machine and its fixturing. Other sources of variation end to cause changes in the output only
over along period of time, either gradually as with tool or machine wear, step with procedural changes, or
irregularly, as with environmental changes such as power surge. Therefore the time period and condition over a
which measure are made will effect the amount of the total variation that will be present.
Common cause refer to the many sources of variation within a process that has a stable and repeatable
distribution over a time. This is called “STATE
of STATISTICAL CONTROL” .
Common cause behave like a stable system of chance cause. If only common cause of variation are present and
do not change, the output of a process is predictable.
The change in the process due to the SPECIAL cause can either be detrimental or beneficial. When detrimental,
they need to be identified and removed. When beneficial, they should be identified and made a permanent part
of the process.
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SPECIAL CAUSE
COMON CAUSE
LOCAL ACTION
ACTION on SYSTEM
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CONTROL CHART
When you need to discover how much variability in a process is due to
unique events/individual actions in order to determine whether a
PROCESS IS IN STATISTICAL CONTROL
Variable Data
X bar - R chart
X-s Chart
X- Mr Chart
Attribute Data
p Chart
np Chart
c Chart
u chart
Statistical Process Control
X =
X+X+X+…X
1 2 3
n
n
R =
R+R+R+…R
1
2
3
n
n
Upper Control Limit
Lower Control Limit
UCL = X + A2R
LCL = X - A 2R
Center Line for Average Chart is X double bar
and
Center line for Range chart is R bar
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The p Chart = Proportion Defective
Number of rejects in a subgroup
p =
Number inspected in subgroup
_
p =
Total Number of rejects
Total Number inspected
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INTERPRETING CONTROL CHARTS
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COMMON QUESTION TO ASK
WHEN INVESTIGATING AN
OUT OF CONTROL PROCESS
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Process Capability
Cp =
Tolerance band
6*
Cpk =
Min of

(USL-X d bar), (X d bar - LSL)
3* 
3* 