Have you ever

1
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

• 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 8 9

• Deviation distance between observations and the
  mean (or average)

Emmett
Observations
10
9
8
8
7
averages 8.4
Deviations
10 - 8.4 1.6
9 8.4 0.6
8 8.4 -0.4
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
7
7
6
6
averages 6.6
Deviations
7 6.6 0.4
7 6.6 0.4
7 6.6 0.4
6 6.6 -0.6
6 6.6 -0.6
0.0
7 6 7 7 6
Jake
6
Variability
8 7 10 8 9

• Variance average distance between observations
  and the mean squared

Emmett
Observations
10
9
8
8
7
averages 8.4
Deviations
10 - 8.4 1.6
9 8.4 0.6
8 8.4 -0.4
8 8.4 -0.4
7 8.4 -1.4
0.0
Squared Deviations
2.56
0.36
0.16
0.16
1.96
1.0
Jake
7
Variability

• Variance average distance between observations
  and the mean squared

Emmett
Observations
7
7
7
6
6
averages
Deviations






Squared Deviations






7 6 7 7 6
Jake
8
Variability

• Variance average distance between observations
  and the mean squared

Emmett
Observations
7
7
7
6
6
averages 6.6
Deviations
7 - 6.6 0.4
7 - 6.6 0.4
7 - 6.6 0.4
6 6.6 -0.6
6 6.6 -0.6
0.0
Squared Deviations
0.16
0.16
0.16
0.36
0.36
0.24
7 6 7 7 6
Jake
9
Variability

• Standard deviation square root of variance

Emmett
Variance Standard Deviation
Emmett 1.0 1.0
Jake 0.24 0.4898979
Jake
10
Variability
The world tends to be bell-shaped
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?

1. One observation falls outside 3 standard
   deviations?
2. One observation falls in zone A?
3. 2 out of 3 observations fall in one zone A?
4. 2 out of 3 observations fall in one zone B or
   beyond?
5. 4 out of 5 observations fall in one zone B or
   beyond?
6. 8 consecutive points above the mean, rising, or
   falling?

1 2 3 4 5 6 7 8
14
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
• Statistical
• Process limits are used for individual items
• Control limits are used with averages
• Limits µ 3s
• 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 lt variance of individual
  items

Distribution of individuals
Process limits
17
Usual v. Unusual, Acceptable v. Defective
B
C
D
E
A
µ
Target
18
More about limits
Good quality defects are rare (Cpkgt1)
µ target
Poor quality defects are common (Cpklt1)
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 (Cpkgt1)
• Poor quality defects are common (Cpklt1)

USL x 3s
24 20 3(2)


.667
Cpk min

x - LSL 3s
20 15 3(2)


.833


3s (UPL x, or x LPL)
20
Going out of control

• When an observation is unusual, what can we
  conclude?

X
21
Going out of control

• When an observation is unusual, what can we
  conclude?

s1
X
22
Setting up control chartsCalculating the limits

1. Sample n items (often 4 or 5)
2. Find the mean of the sample (x-bar)
3. Find the range of the sample R
4. Plot on the chart
5. Plot the R on an R chart
6. Repeat steps 1-5 thirty times
7. Average the s to create (x-bar-bar)
8. Average the Rs to create (R-bar)

23
Setting up control chartsCalculating the limits

1. Find A2 on table (A2 times R estimates 3s)
2. Use formula to find limits for x-bar chart
3. Use formulas to find limits for R chart

24
Lets try a small problem
smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6
observation 1 7 11 6 7 10 10
observation 2 7 8 10 8 5 5
observation 3 8 10 12 7 6 8
x-bar
R
X-bar chart R chart
UCL
Centerline
LCL
25
Lets try a small problem
smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6 Avg.
observation 1 7 11 6 7 10 10
observation 2 7 8 10 8 5 5
observation 3 8 10 12 7 6 8
X-bar 7.3333 9.6667 9.3333 7.3333 7 7.6667 8.0556
R 1 3 6 1 5 5 3.5
X-bar chart R chart
UCL 11.6361 9.0125
Centerline 8.0556 3.5
LCL 4.4751 0
26
X-bar chart
11.6361
8.0556
4.4751
27
R chart
9.0125
3.5
0
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
Interpreting charts

• In the excel spreadsheet, look for these shifts

A
B
D
C
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
• Dont convert measurement data to yes/no
  binomial data (Xs to Ps)
• Not all out-of control points are bad
• Dont combine data (or mix product)
• Have out-of-control procedures (what do I do
  now?)
• Actual production volume matters (Average Run
  Length)