1. spc
Statistical process control Key Quality characteristic :Forecast Error for demand

2. BENEFITS of SPC   
Monitors and provides feedback for keeping processes in control.
Triggers when a problem occurs
Differentiates between problems that are correctable and those that are due to chance. Gives you better control of your process.
Reduces need for inspection
Provides valuable knowledge in the working of the process

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

4. Have you ever… Who is the better shot? Shot a rifle? Played darts?
Player A
Player B
Who is the better shot?
Shot a rifle?
Played darts?
Shot a round of golf?
Played basketball?

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

6. Variability 8 7 10 9
Deviation = distance between observations and the mean (or average)
Player A
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
Player B

7. 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

8. 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

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

10. 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

11. 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

12. 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

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

14. “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

15. 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

16. 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

17. 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

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

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

20. 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.

21. 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)

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

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

24. The SPC implementation process
Identify what characteristics to be controlled
Establish Control limits
Find how to control the process
Learn how to measure improvement of a process
Learn how to detect shift and how to set alerts that take action.
Learn about the two types of causes that affect your variation.

25. 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 x bar on the x bar chart
Plot the R on an R chart
Repeat steps 1-5 thirty times
Average the x bars to create (x-bar-bar)
Average the R’s to create (R-bar)

26. 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:

27. 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

28. 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

29. R chart
9.0125
3.5

30. X-bar chart
8.0556
4.4751

31. AP Uploads Quality control

32. 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

33. 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

34. 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)

35. SPC Station

36. SPC as a triggering tool

37. 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

38. 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)

39. Statistical Process Control (S.P.C.)
This is a control system which uses statistical techniques for knowing, all the time, changes in the process.
It is an effective method in preventing defects and helps continuous quality improvement.

40. What does S.P.C. mean? Statistical:
Statistics are tools used to make predictions on performance.
There are a number of simple methods for analysing data and, if applied correctly, can lead to predictions with a high degree of accuracy.

41. What does S.P.C. mean? Process:
The process involves people, machines, materials, methods, management and environment working together to produce an output, such as an end product.

42. What does S.P.C. mean? Control:
Controlling a process is guiding it and comparing actual performance against a target.
Then identifying when and what corrective action is necessary to achieve the target.

43. S.P.C.
Statistics aid in making decisions about a process based on sample data and the results predict the process as a whole.

44. Machines
Material
People
Output
Management
Methods
Environment

45. The Aim of S.P.C. - Prevention Strategy
Prevention Benefits:
Improved design and process capability.
Improved manufacturing quality.
Improved organisation.
Continuous Improvement.

46. S.P.C. as a Prevention Tool
The S.P.C. has to be looked at as a stage towards completely preventing defects.
With stable processes, the cost of inspection and defects are significantly reduced.

47. The Benefits of S.P.C. Assesses the design intent.
Achieves a lower cost by providing an early warning system.
Monitors performance, preventing defects.
Provides a common language for discussing process performance.

48. Process Variations Process Element Variable Examples
Machine………………………….Speed, operating temperature, feed rate
Tools………………………………..Shape, wear rate
Fixtures…………………………..Dimensional accuracy
Materials…………………………Composition, dimensions
Operator…………………………Choice of set-up, fatigue
Maintenance…………………Lubrication, calibration
Environment…………………Humidity, temperature

49. Process Variations
No industrial process or machine is able to produce consecutive items which are identical in appearance, length, weight, thickness etc.
The differences may be large or very small, but they are always there.
The differences are known as ‘variation’. This is the reason why ‘tolerances’ are used.

50. Stability
Common causes are the many sources of variation that are always present.
A process operates within ‘normal variation’ when each element varies in a random manner, within expected limits, such that the variation cannot be blamed on one element.
When a process is operating with common causes of variation it is said to be stable.

51. Process Control
The process can only be termed ‘under control’ if it gives predictable results.
Its variability is stable over a long period of time.

52. Process Control Charts
Graphs and charts have to be chosen for their simplicity, usefulness and visibility.
They are simple and effective tools based on process stability monitoring.
They give evidence of whether a process is operating in a state of control and signal the presence of any variation.

53. Consider these 50 measurements
Data Interpretation
Consider these 50 measurements

54. Data Interpretation
As a set of numbers it is difficult to see any pattern.
Within the table, numbers 30 and 37 were outside the tolerance – but were they easy to spot?
A way of obtaining a pattern is to group the measurements according to size.

55. Data Interpretation – Tally Chart
The tally chart groups the measurements together by size as shown.
The two parts that were out of tolerance are now easier to detect (36.38mm).

56. Tally Chart - Frequency2
The tally chart shows patterns and we can obtain the RANGE mm to 36.38mm.
The most FREQUENTLY OCCURRING size is 36.35mm. 6 7 16 12 5 2

57. Tally Chart - Information
The tally chart gives us further information:
The number of bores at each size;
The number of bores at the most common size;
The number of bores above and below the most common size (36.35mm) -
number above 36.35mm is 7+6+2=15
number below 36.35mm is =19

58. We can redraw the frequency chart as a bar chart known as a histogram: