1. DSQR Training Process Capability & Performance
HEATING, COOLING & WATER HEATING PRODUCTS
DSQR Training Process Capability & Performance
Fred Nunez
Corporate Quality

2. Goals At the end of this section you’ll be able to
Process Capability
At the end of this section you’ll be able to
apply the basic methods for assessing process capability (Cp, Cpk, Pp, Ppk).
use the properties of a Normal Curve that are important to process capability calculations.
explain the Minitab “6pack” and Minitab capability report for the Normal distribution case.

3. Process Capability Indices
Process capability and performance indices are ways for measuring how the process distribution is aligned with the specification.
USL
LSL
Voice of the Customer
Voice of the Process
-3s
+3s

4. Process Capability What shall we do?
15 % above the Upper Spec Limit
3 % below the Lower Spec Limit
Normal process variation
This is an example of a situation where the distribution of values for this in-control process does not fall within the allowable tolerances.
What shall we do?
Since this process is in-control but not capable, one of three actions must occur:
Change the specifications
“Suffer and Sort”
Make a fundamental change to the process
Don’t tell anyone

5. Process Capability
Process Capability
Here is a situation in which the process average is on-target, but the spread of the values are barely within allowable tolerances.
Target
But if we only control process variability but don’t control the process average, we might get this.
Target
And if we control process average only, and fail to control process variability, we might get this. 5

6. The Normal Curve and Process Capability
When continuous data are normally distributed, calculating a process capability index is really equivalent to finding the area under the normal (or bell-shaped) curve that is outside the spec limits, as depicted in the diagram below.
LSL
USL
The normal curve can provide a good model for process observations, but the model does not apply to every situation. The usual measures and interpretation of process capability depend on the properties of the normal curve.

7. Normal Distribution –3S +3S +2S +1S –2S –1S 34.13% 13.60% 2.14% 0.13%
Process Capability
Normal Distribution
–3S
+3S
+2S
+1S
–2S
–1S
34.13%
13.60%
2.14%
0.13%
As you can see, the curve is divided into a series of equal increments, each representing one standard deviation from the mean.
The area under the curve represented by the first standard deviation out from the center in either direction represents approximately 34% of the total area. Together, the area represented within one standard deviation of the center is about 68% of the total area. In other words, given a data set that is normally distributed, approximately 68% of the data values should fall within one standard deviation of the center.
Going out plus or minus two standard deviations represents approximately 95% of the total area; go out 3 standard deviations in either direction and you’ve accounted for more than 99% of the area.
Tables have been developed that contain these listed areas, plus many more.
Thus by knowing a normal curve’s mean and standard deviation, we can figure out the yields within specified “zones.”
68.26%
95.46%
99.73%

8. Common Process Capability Indices: The C and P families
Pp - Process Performance
This is the performance index which is defined as the tolerance width divided by the performance, irrespective of process centering.
Remember that this discussion applies equally to both Pp and Cp.
Since is a “P” family, it used the standard deviation of all the data to estimate variation.
If it was the “C” family, it would have used the average range from a control chart to estimate variation.
Where: USL = upper specification limit
LSL = lower specification limit
6s = 6 times the sample standard
deviation

9. Common Process Capability Indices: The C and P families
Pp - Process Performance
You can think of Pp as a measure of how many times the process spread will go into the tolerance.
The high the quotient, the better. This implies that the spread is small compared to the tolerance.
Pictorially, the process performance Pp is the tolerance width divided by the process spread.

10. Common Process Capability Indices: The C and P families
Pp - Process Performance
The Pp is determined by the tolerance and spread of the process, location is not considered.
The red (left) and blue (right) distributions have the same Pp.
Virtually all of the parts produced on the red (left) process will be in specification, while virtually all of the parts from the blue (right) process will be out of specification.
Important to realize that the location of the distribution has no impact on the Pp (Cp) calculation.

11. Common Process Capability Indices: The C and P families
Ppk - Process Performance
The process performance index, Ppk,, which accounts for process centering and is defined as:
Pp (Cp) did not consider location in the calculations.
Ppk (Cpk) is influenced by the location of the distribution.
To estimate the Ppk perform both calculation above and report the smaller value. A quicker way is to determine which specification limit (USL or LSL) is closest to the average and only do that calculation, it will be the smallest.

12. Common Process Capability Indices: The C and P families
Ppk - Process Performance
The Ppk is determined by the tolerance, spread and distance from specification.

13. Common Process Capability Indices: The C and P families
Ppk - Process Performance
Here we can see the impact of the specification in the definition of Ppk.
Both processes above will have the same Pp, same spread and tolerance.
The Ppk for the blue (left) process will be lower because (Xbar-LSL) is smaller.

14. Interpreting Ppk 14 LSL USL LSL USL
Process Capability
Interpreting Ppk
LSL
USL
LSL
USL
Ppk ~ 2.0
Ppk ~ 0.4
Ppk ~ 1.3
Ppk ~ 0.0
Ppk ~ 1.0
Ppk ~ -1.0
Notice that although the variability is the same for each distribution and Pp=2.0, Ppk changes dramatically depending on where the process is centered. 14

15. Common Process Capability Indices: The C and P families
Cp, Cpk, Pp, Ppk
The only difference between the C and P capability indices is the method used to estimate the standard deviation.
When you see an index with a “C” the standard deviation was estimated using the average range from a control chart.
When you see an index with a “P” the standard deviation was estimated using the standard deviation of all the data.
Both calculations assume that the data is normally distributed.

16. Ppu or Ppl vs. Amount Out-of-Spec
Process Capability
Ppu or Ppl vs. Amount Out-of-Spec
Ppu or Ppl
% Out-of-Spec
p.p.m. Out-of-Spec
These values apply only to the tail of the distribution with the higher % out-of-spec (smaller index).
Actual % out-of-spec may be as much as double these values when both tails (upper & lower) are considered. 16

17. Common Process Capability Indices: The C and P families
Index Symbol
Index Name
Default Formula in Minitab
Notes
(Normal Distribution Case) C
Capability Index (
USL-LSL)/6 swithin
The index is not defined p
unless both the upper and
lower specification limits are
used. P
Performance Index p (
USL-LSL)/ 6 soverall
The index is not defined
unless both the upper and
lower specification limits are
used.
CPU
Upper Capability (
USL- X
)/3 swithin
Index
PPU
Upper Performance (
USL- X
)/3 soverall
Index
Different software programs will use different algorithms to estimate sigma.
You may get a slightly different estimate using the same data in Excel, Statgraphics or Minitab.
CPL
Lower Capability ( X -
LSL)/3 swithin
Index
PPL
Lower Performance ( X -
LSL)/3 soverall
Index C
Capability Index
Minimum of {
CPU,CPL}
Cpk takes into account the pk
process center while
Cp does
not. P
Performance Index
Minimum of {
PPU,PPL}
Ppk takes into account the pk
process center while
Pp does 17
not.

18. Process Capability Statistics
Data: C:\SixSigma\Data\pHexample.mtw
Use the following Minitab command to obtain descriptive statistics:
Stat>Basic Statistics> Graphical Summary
Situation: 100 hourly batch values after one day ramp up, following major replacement of process equipment. The product is pH buffer solution which is supposed to measure 4.0 ± 0.02 at 25° C. 18

19. Process Capability Statistics19
The TrMean is calculated after removing the highest & lowest 5%. The SE Mean is the standard error of the mean; the standard deviation of the distribution of the means – Central Limit Theorem.

20. Process Capability Statistics
Data: C:\SixSigma\Data\pHexample.mtw
Use the following Minitab command to compute the process capability statistics:
Stat>Quality Tools>Capability Analysis (Normal)
Enter these values 20

21. Process Capability Statistics
Mean
Standard Deviation
Specification
Cp & Cpk
Pp & Ppk
Actual Observed PPM
Estimated PPM 21

22. Process Capability
Capability Sixpack
Data: C:\SixSigma\Data\pHexample.mtw
Use the following Minitab command to compute the create the Sixpack analysis:
Stat>Quality Tools>Capability Sixpack (Normal)
Data: C:\SixSigma\Data\pHexample.mtw
Use the following Minitab command to compute the process capability statistics: Stat>Quality Tools>Capability Sixpack (Normal) 22
Situation: 100 hourly batch values after one day ramp up, following major replacement of process equipment. The product is pH buffer solution which is supposed to measure 4.0 ± 0.02 at 25° C.

23. Capability Sixpack 23 See next slide Enter these values
Process Capability
Capability Sixpack
See next slide
Enter these values 23

24. Capability Sixpack, cont.
Process Capability
Capability Sixpack, cont.
You may select all the test or only one.
For subgroup size >1, default is pooled standard deviation to obtain denominator in C family 24

25. Process Capability Sixpack for Production pH2 1 4 3
1. The control charts show no signals of special causes, so the C and P family indices should give about the same values.
2. The individual observations match the reference line, so the normal distribution will provide a useful model.
3. The capability plot shows how well the process is centered as well as shows the amount of tolerance used by the process.
As Cp is about 1.0, the short-term process tolerance length is about the same length as the distance between upper and lower specifications.
It is worth noting that Minitab uses different estimates for sigma than AIAG.

26. Process Capability Sixpack for Production pH
The control charts show no signals of special causes, so the C and P family indices should give about the same values.
The individual observations match the reference line, so the normal distribution will provide a useful model.
The capability plot shows how well the process is centered as well as shows the amount of tolerance used by the process.
As Cp is about 1.0, the short-term process tolerance length is about the same length as the distance between upper and lower specifications.

27. Application Exercise – Process Capability
Which two processes are the most variable?
__________ and _________
2. Which two processes are not potentially capable?
__________ and _________ a
3. Which two processes have the highest % out-of-spec?
__________ and _________. b
4. Which process has the highest Cp?
__________ c
5. For which three processes are Cpk and Cp equal?
__________, ________ and ____________
6. Which process is potentially capable but not meeting specs?
__________ d
7. Which process is supplying the most material at target value?
__________ e
8. If these materials were stored in the warehouses of six different suppliers (all other things being equal) which one would you prefer?
__________ f
9. If the process average could be adjusted for future production, which supplier would you prefer?
__________
10. Calculate Cp and Cpk for c) & d).

28. Application Exercise – Process Capability
Which two processes are the most variable?
__________ and _________ e f
2. Which two processes are not potentially capable?
__________ and _________ e f a
3. Which two processes have the highest % out-of-spec?
__________ and _________. c f b
4. Which process has the highest Cp?
__________ d
Cp=1.00
Cpk=0.53
5. For which three processes are Cpk and Cp equal?
__________, ________ and ____________ c a b e
6. Which process is potentially capable but not meeting specs?
__________ c d
Cp=2.00
Cpk=1.33
7. Which process is supplying the most material at target value?
__________ a
8. If these materials were stored in the warehouses of six different suppliers (all other things being equal) which one would you prefer?
__________ e a
9. If the process average could be adjusted for future production, which supplier would you prefer?
__________ f d
10. Calculate Cp and Cpk for c) & d). 28

29. Process Capability and Normality
The calculated capability indices and the corresponding % out-of-spec values are only valid when the individual data points are normally distributed.
Special causes tend to distort the Normal curve. 29