1. What is the point of these sports?
Have you ever…
Shot a rifle?
Played darts?
Played basketball?
Shot a round of golf?
What is the point of these sports?
What makes them hard?

2. Have you ever… Who is the better shot? Shot a rifle? Played darts?
Emmett
Jake
Who is the better shot?
Shot a rifle?
Played darts?
Shot a round of golf?
Played basketball?

3. Discussion What do you measure in your process?
Why do those measures matter?
Are those measures consistently the same?
Why not?

4. Variability 8 7 10 9
Deviation = distance between observations and the mean (or average)
Emmett
Observations 10 9 8 7
averages
8.4
Deviations
= 1.6
9 – 8.4 = 0.6
8 – 8.4 = -0.4
7 – 8.4 = -1.4
0.0
Jake

5. Variability
Deviation = distance between observations and the mean (or average)
Emmett
Observations 7 6
averages
6.6
Deviations
7 – 6.6 = 0.4
6 – 6.6 = -0.6
0.0 7 6
Jake

6. Variability 8 7 10 9
Variance = average distance between observations and the mean squared
Emmett
Observations 10 9 8 7
averages
8.4
Deviations
= 1.6
9 – 8.4 = 0.6
8 – 8.4 = -0.4
7 – 8.4 = -1.4
0.0
Squared Deviations
2.56
0.36
0.16
1.96
1.0
Jake
Variance

7. Variability
Variance = average distance between observations and the mean squared
Emmett
Observations 7 6
averages
Deviations
Squared Deviations 7 6
Jake

8. Variability
Variance = average distance between observations and the mean squared
Emmett
Observations 7 6
averages
6.6
Deviations
= 0.4
6 – 6.6 = -0.6
0.0
Squared Deviations
0.16
0.36
0.24 7 6
Jake
Variance

9. But what good is a standard deviation
Variability
Standard deviation = square root of variance
Emmett
Variance
Standard Deviation
Emmett
1.0
Jake
0.24
Jake
But what good is a standard deviation ?

10. Variability The world tends to be bell-shaped Even very rare
outcomes are
possible
(probability > 0)
Fewer
in the
“tails”
(lower)
(upper)
Most outcomes
occur in the
middle

11. Variability Here is why:
Even outcomes that are equally likely (like dice), when you add them up, become bell shaped

12. “Normal” bell shaped curve
Add up about 30 of most things
and you start to be “normal”
Normal distributions are divide up
into 3 standard deviations on
each side of the mean
Once your that, you
know a lot about
what is going on ?
And that is what a standard deviation
is good for

13. Usual or unusual? One observation falls outside 3 standard deviations?
One observation falls in zone A?
2 out of 3 observations fall in one zone A?
2 out of 3 observations fall in one zone B or beyond?
4 out of 5 observations fall in one zone B or beyond?
8 consecutive points above the mean, rising, or falling? X X XX
X X
X X XX

14. SPC uses samples to identify that special causes have occurred
Causes of Variability
Common Causes:
Random variation (usual)
No pattern
Inherent in process
adjusting the process increases its variation
Special Causes
Non-random variation (unusual)
May exhibit a pattern
Assignable, explainable, controllable
adjusting the process decreases its variation
SPC uses samples to identify that special causes have occurred

15. Limits Process and Control limits: Specification limits: Statistical
Process limits are used for individual items
Control limits are used with averages
Limits = μ ± 3σ
Define usual (common causes) & unusual (special causes)
Specification limits:
Engineered
Limits = target ± tolerance
Define acceptable & unacceptable

16. Process vs. control limits
Distribution of averages
Control limits
Specification limits
Variance of averages < variance of individual items
Distribution of individuals
Process limits

17. Usual v. Unusual, Acceptable v. Defectiveμ
Target

18. Cpk measures “Process Capability”
More about limits
Good quality: defects are rare (Cpk>1) μ
target
Poor quality: defects are common (Cpk<1) μ
target
Cpk measures “Process Capability”
If process limits and control limits are at the same location, Cpk = 1. Cpk ≥ 2 is exceptional.

19. Process capability Good quality: defects are rare (Cpk>1)
Poor quality: defects are common (Cpk<1) =
USL – x 3σ
24 – 20
3(2) = =
.667
Cpk = min =
x - LSL 3σ
20 – 15
3(2) = =
.833 = =
3σ = (UPL – x, or x – LPL)

20. Going out of control
When an observation is unusual, what can we conclude? μ2
The mean
has changed X μ1

21. Going out of control
When an observation is unusual, what can we conclude?
The standard deviation
has changed σ2 σ1 X

22. Setting up control charts: Calculating the limits
Sample n items (often 4 or 5)
Find the mean of the sample (x-bar)
Find the range of the sample R
Plot on the chart
Plot the R on an R chart
Repeat steps 1-5 thirty times
Average the ’s to create (x-bar-bar)
Average the R’s to create (R-bar)

23. Setting up control charts: Calculating the limits
Find A2 on table (A2 times R estimates 3σ)
Use formula to find limits for x-bar chart:
Use formulas to find limits for R chart:

24. Let’s try a small problem
smpl 1
smpl 2
smpl 3
smpl 4
smpl 5
smpl 6
observation 1 7 11 6 10
observation 2 8 5
observation 3 12
x-bar R
X-bar chart
R chart
UCL
Centerline
LCL

25. Let’s try a small problem
smpl 1
smpl 2
smpl 3
smpl 4
smpl 5
smpl 6
Avg.
observation 1 7 11 6 10
observation 2 8 5
observation 3 12
X-bar
7.3333
9.6667
9.3333
7.6667
8.0556 R 1 3
3.5
X-bar chart
R chart
UCL
9.0125
Centerline
8.0556
3.5
LCL
4.4751

26. X-bar chart
8.0556
4.4751

27. R chart
9.0125
3.5

28. Interpreting charts
Observations outside control limits indicate the process is probably “out-of-control”
Significant patterns in the observations indicate the process is probably “out-of-control”
Random causes will on rare occasions indicate the process is probably “out-of-control” when it actually is not

29. Show real time examples of charts here
Interpreting charts
In the excel spreadsheet, look for these shifts: A B C D
Show real time examples of charts here

30. Lots of other charts exist
P chart
C charts
U charts
Cusum & EWMA
For yes-no questions like “is it defective?” (binomial data)
For counting number defects where most items have ≥1 defects (eg. custom built houses)
Average count per unit (similar to C chart)
Advanced charts
“V” shaped or Curved control limits (calculate them by hiring a statistician)

31. Selecting rational samples
Chosen so that variation within the sample is considered to be from common causes
Special causes should only occur between samples
Special causes to avoid in sampling
passage of time
workers
shifts
machines
Locations

32. Chart advice Larger samples are more accurate
Sample costs money, but so does being out-of-control
Don’t convert measurement data to “yes/no” binomial data (X’s to P’s)
Not all out-of control points are bad
Don’t combine data (or mix product)
Have out-of-control procedures (what do I do now?)
Actual production volume matters (Average Run Length)