This presentation gives a basic overview of statistical process control with emphasis on the sections of a chart and interpretation of charts

1. Overview of Statistical
Process Control (SPC)
March 18, 2009

2. SPC Defined
• Basic
– Shows the behavior of a characteristic over time
– Shows the influence of different variables on the
characteristic
– Shows where the process is located and how much
variation is present in the process
– Helps us get a process in a state of control
• Advanced
– Is the basis for establishing process capability
• Process capability defines how well (or not well) our process
can meet the needs of our customers
– Separates common cause variation from special
cause variation
2

3. Process Limits-Not Customer Limits
If the process remains stable and in control, we expect the
process’ output to run between these limits almost 100% of
the time. 3

4. The Relationship of Process Limits to
Customer Limits (Process Capability)
The process limits are wider than the customer’s
The process limits are tighter than the customer’s
limits. The process is not capable. You have three
limits. This is a capable process and no significant
options: Get your customer to relax his
action is needed other than make sure the process
requirement, 100% inspect the output of the
is followed.
process, or change the process to meet the
customer’s requirements
The process limits are marginally better than the customer’s The process limits are tighter than the customer’s limits but
limits. The process is centered so variation must be the process is off target (to high side). Adjust process to 4
reduced. Great case for six sigma. target. If the process can’t be adjusted, then reduce variation.
Great case for six sigma

5. Common Cause and Special Cause
Variation
Lower Process Limit Upper Process Limit
• Common cause variation is
what we expect to happen
99.97% of the time if the
process is in control.
• Common cause variation
exists between the process
limits
• Special cause variation is not
expected to happen and has
assignable causes.
• Special cause variation occurs
outside the process limits
99.97%
5

6. Common Cause Special Cause
Variation Variation
Histogram of Process Week One Histogram of Process Week One
20 14
12
15
10
If only common cause
Frequency
Frequency
8
10
variation is present in
6
5 4
the process, the
2
0
1.68 1.76 1.84 1.92 2.00 0
histogram will look the
Peen Height 1.68 1.74 1.80 1.86 1.92 1.98
Peen Height
Histogram of Process Week Two
Histogram of Process Week Two
same over time
12
12
10
10
8
8
Frequency
Frequency
6
6
If special cause
4
4
2
2
variation exists, the
0
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0
1.68 1.74 1.80 1.86 1.92 1.98 Peen Height
histogram will change
Peen Height
Histogramof Process W Three
eek
18
over time in location
Histogram of Process Week Three
16
4
14
and/or spread
12
3
Frequency
10
Frequency
8 2
6
4 1
2
0
0
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
Peen Height
Peen Height
6

7. Examples of Common
Cause/Special Cause Variation
• Body Temperature
– If our body’s processes are in control, we expect temperature to vary slightly
above and below 98.6 degrees F. This is the common cause (or expected)
variation.
– If a virus (special cause) enters our body, a process will be altered and
temperature will spike significantly high
• Teenage Behavior
– Teenagers do teenage things. Always have and always will. Parents must
decide what is expected behavior and what is not expected behavior. The
former (good or bad) usually warrants a stern lecture while the latter deserves
punishment.
– Special causes often drive teenage behavior. The breakup by a girlfriend. Being
cut from a sports team. Making a bad grade. If they are not acting as expected,
we often must find the special cause before acting in return.
– An example-My eighteen year old often challenges me on my philosophies and
opinions. That is fine. I expect him to do that. I’m glad he does it. Sometimes
he goes too far with his mother and can be disrespectful. That’s outside the
boundaries of normal behavior and incurs my wrath.
7

8. Exercise #1
• Run product from machine determine
upper and lower process limits
• Run product to see how the process limits
hold
• Introduce special causes
– Increased standard deviation
– Shift in average
8

9. The Sections of a Control Chart:
Process Information
• Process information:
This is needed to keep
production records to go
along with the data.
• What you should record:
– Date data was collected
– Time data was collected
– Who collected the data
9

10. The Sections of a Control Chart:
Subgroups
• The data is recorded in subgroups
• The subgroups are set up to be a
certain size. The size of a
subgroup is the number of
readings recorded.
– Typical sizes are three and
five
• A completed control chart is one
with at least twenty completed
subgroups on the page
10

11. The Sections of a Control Chart:
Subgroup Statistics
• Once the data is recorded in the
subgroups, we need to perform
calculations for each subgroup
– A measure of where the process
is located. The mean (or average)
X shows us where the process is
located
– A measure of how much variation
is in the process. The range
R
shows us how much variation is in
the process.
11

12. What is a Mean?
• The mean is the
center of weight for
data. Also called
average.
50% 50%
Weight Weight
Mean
12

13. How to Calculate a Mean
• Add up the measurements
and divide by the number
of measurements
– Add up measurements:
o 1.81+1.81+1.82
o Sum=5.44
o Number of measurements: 3
– Divide sum by the number of
measurements
5.44
= 1.813
3
Note: Always record the mean to 1.82
one more decimal place than the
1.813 13
original data point

14. What is a Range?
• The range indicates
how similar (or dis-
Largest
similar) the measurement:
1.80
measurements are in
Smallest
a subgroup measurement:
• To calculate the 1.75
range Range:
1.80-1.75=0.05
– Subtract the smallest
measurement from the
largest measurement
14

15. Exercise #2
• Collect subgroups of data
• Calculate mean and range
15

16. Overall Mean X
1 2 45 6 78 9 10
3
27.16
Number of means:10 Sum:2.73+2.71+2.72+2.72+2.72+2.72+2.70.2.72+2.71+2.71
= 2.716
10
Sum=27.16
16
Divide sum by number of means

17. Overall Range R
• Number of ranges: 10
• Sum of ranges:
o 0.09+0.05+0.05+0.06+0.12+0.08+0.08+0.06+0.07+0.04
o Sum=0.7
o Divide Sum by number of ranges 0.7 = 0.07
10
17

18. Sections of a Control Chart: Plot of
Means and Ranges
Plot of
X
Means
Plot of
R
Ranges
•The plots show
how the process is
behaving over time
•We expect the
points to fall above
and below the
18
center line which is
the overall mean

19. Sections of the Control Chart:
Control Limits
• Control limits are calculated for means
and ranges
• Control limits represent the boundaries
between normal and abnormal
variation or common cause from
special cause variation
• Common cause variation is:
– What we expect to happen the majority
of time.
– Common cause variation is everything
between the limits. You can also call it
50/50 variation. When you flip a coin,
there is a 50% chance of getting a
head and a 50% chance of getting a
tail. Meaning, the only thing driving the
outcome is chance. Same with
production. If only common cause
variation is present, there is a 50%
chance of being above the target and a
50% chance of being below the target.
The majority of points should fall within
the limits.
19

20. Exercise #3
• Collect more subgroups and calculate
control limits
20

21. Interpreting Charts
• There are different pictures you might see
in the plots of means and ranges.
• Key point: Look for abnormal patterns in
the data. Something is causing the
abnormal pattern. This “something” is
called a assignable cause.
21

22. Interpreting Control Charts and
Taking Action
• The averages are
randomly falling above
Process In Control with Chance Variation
and below the centerline.
15 • There are no points
outside the upper control
10 limit.
• The variation is common
5 cause variation. No
X
special causes of
0 variation are present
22

23. Trends
• The plot of averages was
behaving randomly but
Trends
something occurred to
make the process start
drifting upward.
1500 • The process is no longer
behaving randomly.
1000 Special cause variation is
present
• Find the assignable
500
X
cause
• Document your actions
0 on the control chart
23

24. Jumps in Process Level
• The process is not
exhibiting random
Jumps in Process Level
behavior
• Special cause
1500
variation exists
1000 • Find the assignable
cause
500 • Document your
actions on the control
0 chart
24

25. Cyclic Pattern
• There is a repeating
cycle to the data
Recurring Cycles
• This is not random
600 behavior
• Find the assignable
400
cause
200 • Document your
actions on the control
0
chart
25

26. Point Near the Control Limit
• Point at the upper control
limit but not outside the
1500 upper control limit
• Proper action to take:
1000 – Pull another sample and
plot the average and range.
If the average is still near
500 the upper limit, action may
be needed
– Document your actions on
0 the control chart
26

27. Point Well Outside the Upper Limit
• This is a strong signal
that an assignable
Process In Control with Chance Variation
cause exists for this
special cause
1500 variation
• Find the assignable
1000
cause
500 • Document your
actions on the control
0 chart
27

28. Point Just Above or Just Below
Control Limit
• Don’t take the limit so literally.
Remember, there is a small
probability of a point falling
Process In Control with Chance Variation
outside the limit. We can
expect this to happen less than
1% of the time.
1500 • Proper action to take:
– Don’t be so quick to adjust the
1000 machine or process
– Pull another sample and plot
the average and range. If the
500 average is still near the upper
limit, action may be needed
– Document your action on the
0 control chart
28

29. Taking and Documenting Action
• When special cause
variation is present,
find and eliminate the
assignable cause
• Document the actions
taken on the control
chart. Record the
date and time for the
action
29

30. Exercise #4
• Collect more subgroups and evaluate
chart
– Change in process level
– OOC point
30