1. 13.0 PROCESS CAPABILITY SPECIAL TOPICS
Cpk or Ppk?
Cp or Pp? X
LSL
USL
NOMINAL
UCLx
LCLx X

2. 13.0 Process Capability Special Topics
Purpose
Objectives
Short-term versus Long-term Capability Studies
Cp vs. Pp
Cpk vs. Ppk
Relationship to Control Charts
Capability Studies for Bilateral Tolerances
Capability Studies for Unilateral Tolerances
Six-Sigma Quality
Summary

3. Purpose
To learn about the difference between conventional process capability indexes Cp & Cpk and newer indexes Pp & Ppk.
Some SPC software programs calculate all types. When to use a particular index?
Gain an understanding what constitutes a Short-term (potential) variability study versus long-term (performance) variability study.
Learn an approach for assessing Process Capability for Unilateral Tolerances as well as Bilateral Tolerances.

4. Objectives
The method of calculating sigma plays a very important role between short-term (Cp, Cpk) and long-term (Pp, Ppk) capability studies.
How the different process capability indexes (Cp, Cpk, Cpu, Cpl, Pp, Ppk) tie into control charts.
How the different process capability indexes (Cp, Cpk, Cpu, Cpl, Pp, Ppk) tie into gage and machine capability studies.

5. Short-term vs. Long-term Capability Studies
Which Sigma do we use to calculate capability indexes?
Cp, Cpk, Cpu, Cpl utilize sigma-hat above in their calculation.
Pp & Ppk utilize the sum-of-squares sigma in their calculation.
Which do you use (especially since many SPC software programs automatically calculate process capability indexes using both types of sigma)?
Are there different uses for each?
What are the sources of variation for each type of sigma?
What type of capability studies focus on short-term variation?
Where would we utilize long-term capability studies?
What makes up a long-term capability study?
Sigma Estimate
from Control Chart
(SHORT-TERM) d 2 R = M
i= 1 n
(X - X)
n-1 i 2 =
or Sum-of-Squares Sigma =
(LONG-TERM)

6. Short-term Capability Study - Cp
Measure of Process Precision
Cp = Process Potential Index
Formula: Cp = Engineering Tolerance/Natural Tolerance
Where: ET = Upper Specification Level - Lower Specification Level
NT = Natural Tolerance = 6 X Sigma
Sigma = Average Range/d2
What's it used for:
Measures the short-term process precision for a given Key Characteristic - essentially it measures Machine Capability
Short-term process capability is computed using the short-term process variation (Rbar/d2).
This is the machine and gage variation at a certain moment in time (last pieces made)
If the gage variation, as measured by a gage capability study, is less than 20%.....
.....we can conclude the key process input driving the variation in the short-term is the machine.
What question does Cp ask?
Does the process have the precision to potentially make every part 100% to blueprint specification at this moment in time?
GOAL: Cp greater than or equal to 1.33 (equates to a 63 DPM rate or better).

7. Short-term Capability Study - Cpk, Cpl & Cpu
Measure of Process Accuracy
Cpk = Process Potential Index that Accounts for Centering
Formula:
What's it used for:
Measures the short-term process accuracy for a given Key Characteristic - essentially it measures how close to the targeted value the process is running at.
Cpk is the smaller of Cpl or Cpu, depending which side of the tolerance the process is shifted towards.
Cpk should be compared to Cp. The closer Cpk is to Cp, the more centered the process is running.
Cpk is affected by different operators, shifts, raw materials, tool adjustments as well as machine and gage error.
What questions does Cpk ask?
Is the process targeted to the NOMINAL dimension, i.e.., is the process centered?
If a shift is present within the process, should I be concerned?
Cpl
Cpu
Cpk = Minimum
Process Average (Xbar) - Lower Spec. Limit (LSL)
Three Sigma ( ) or
Upper Spec. Limit (USL) - Process Average (Xbar)
Three Sigma ( )
GOAL: Cpk greater than or equal to 1.33 (equates to a 63 DPM rate or better).

8. Long-term Capability Study - Pp
Pp = Process Performance Index
Formula: Pp = Engineering Tolerance/Natural Tolerance
Where: ET = Upper Specification Level - Lower Specification Level
NT = Natural Tolerance = where
What's it used for:
Measures the long-term process precision for a given Key Characteristic - includes all sources of variation and all turnbacks
Long-term process capability is computed using the long-term process variation ( ).
This index measures the performance of the process over a 3-6 month period, usually encompasses data points, three or more set-ups, multiple shifts and multiple operators.
This index should be used as an aid in the tolerancing decisions made on new and mature programs by IPD Teams, Manufacturing & Design Engineers.
Used to assess whether a process can be considered "certified".
Should be compared to Cp & Cpk and used to measure & prioritize improvement over time.
The challenge:
To get Pp to equal Cp and both above This means we are reducing turnbacks that affect our ability to control the accuracy (location to target) of our process.
Now the short-term (machine) variation equals the long-term variation.
Data from process is more than likely normally distributed.
What question does Pp ask?
Does the process have the precision to potentially make every part 100% to blueprint specification over multiple set-ups, over a 3-6 month period, with different Operators, etc.? M
i= 1 n
(X - X)
n-1 i 2 =
GOAL: Pp greater than or equal to 1.33 (equates to a 63 DPM rate or better).

9. Long-term Capability Study - Ppk
Measure of Process Accuracy
Ppk = Process Performance Index that Accounts for Centering
Formula:
What's it used for:
Measures the long-term process accuracy for a given Key Characteristic - essentially it measures how close to the targeted value the process is running at.
Ppk should be used in producibility studies for tolerancing purposes.
Should be compared to Cp & Cpk and used to measure & prioritize improvement over time.
Can be used to determine machine wear over time; drive TPM event.
Cpk is affected by different operators, shifts, raw materials, tool adjustments as well as machine and gage error.
What questions does Ppk ask?
Is the process targeted to the NOMINAL dimension, i.e.., is the process centered?
If a shift is present within the process, should I be concerned?
Ppk = Minimum
Process Average (Xbar) - Lower Spec. Limit (LSL)
Three Sigma ( ) or
Upper Spec. Limit (USL) - Process Average (Xbar)
Three Sigma ( )
n-1
n-1
GOAL: Ppk greater than or equal to 1.33 (equates to a 63 DPM rate or better).

10. Short-term vs. Long-term Capability Studies Matrix
Cp versus Pp - The difference is Sigma
SHORT-TERM
LONG-TERM
(Within subgroup)
(Between subgroup)
USL - LSL Cp =
USL - LSL Pp = 6
 6
n-1 d 2 R =

(Where )
(Where = Sum-of-Squares Method)
n-1
Machine
Leadscrews
X, Y & Z Axes
Measurement
Gage
Operator
Bias
Machine
Measurement
Raw Materials
SOURCES OF
Time
VARIATION
Different Operators
Adjustments
Shift, etc.
MEASURED BY WHICH
R-Chart
Averages Chart
CONTROL CHART?
s-Chart
Individuals Chart
PRACTICAL
Machine Capability Studies
Manufacturability/Producibility
Gage Capability Studies
for new designs
APPLICATIONS
Initial Lot Qualification
Supplier Certification

11. Relationship to Control Charts
The following examples from XYZ Company Heat Exchanger area are used to illustrate the following key points:
Processes in a state of statistical control, i.e., absent of turnbacks, have the following characteristics:
Cp & Cpk values drive closer to Pp & Ppk values.
Process drives toward a normal distribution.
Short-term variation equaling the long-term variation.
Key sources of variation affecting the process are the machine and the measurement system.
If the measurement system is less than 20%, the key source remaining is the machine.
Processes not in a state of statistical control, i.e., have special causes (turnbacks) present, have the following characteristics:
Cp & Cpk values much higher than Pp & Ppk values.
Non-normal distribution.
Long-term variation generally much greater than the short-term variation.
Process affected by changes in raw materials, temperature, set-up inconsistencies, different Operators, shifts, etc.

12. Capability Studies for Bilateral Tolerances
How do we handle capability analysis for two-sided tolerances?
BILATERAL Dimensions (i.e., Diameters, Linear Dimensions, etc.)
LSL
NOMINAL
USL X
CONVENTIONAL CONTROL CHART CAPABILITY ANALYSIS:
USL - LSL Cp =
Cpk = MINIMUM { Cpl, Cpu }, where: 6

Cpl = X - LSL
Cpu = USL - X R
(Where )

and = d 3 3 2
GOAL: Cp & Cpk > 1.33

13. Capability Studies for Unilateral Maximum Tolerances
ZERO
USL = MAX
EXAMPLES:
Runout
Flatness
True Position
Roundness
Straightness
Perpendicularly X
CAPABILITY ANALYSIS:
Now it is time to change the rules for Cpk analysis as illustrated for Bilateral
tolerances. Since it is assumed smaller values are always superior to larger
values, the most meaningful capability index for MAXIMUM tolerances will be:
Is there a probability of making product beyond
Cpu = USL - X
Cpu ANSWERS:
the Maximum tolerance allowed? 3
GOAL: Cpu > 1.33

14. Capability Studies for Unilateral Minimum Tolerances
LSL = MIN.
EXAMPLES:
Wall Thickness
MTBF
MTTF
Horsepower X
CAPABILITY ANALYSIS:
Since it is assumed larger values are always superior to smaller
values, the most meaningful capability index for MINIMUM tolerances will be:
Is there a probability of making product below
Cpl = X - LSL
Cpl ANSWERS:
the Minimum tolerance allowed? 3
GOAL: Cpl > 1.33

15. Six Sigma Quality - What is is?
As defined by WXY Company, Six-Sigma Quality is a strategy of continuously
improving a process to a point that the process only produces a defect rate of
3.4 parts per million (ppm). This defect rate is characterized by a capability
precision level of Cp = 2.0, and a capability accuracy level Cpk = 1.5.
A process at the Six-Sigma capability level is said to be "ROBUST", such that
variations in the key factors of the process will not produce defects.
LSL
NOMINAL
USL 12
1.5 6 X
GOAL: Cp = 2.0 and Cpk = RESULT: 3.4 PPM Defect Rate

16. Six Sigma Quality - How do we get there?
Utilize Advanced Quality System/Process Certification tools to determine "Critical-to-Quality" and "Key Characteristics".
Use QCPC to remove assignable causes (turnbacks) of variation and SPC control charts to establish process predictability.
Calculate long-term Pp & Ppk, characterized by:
Sum-of-the-squares sigma
Multiple set-ups (at least three)
Multiple Operators (where applicable)
Time (recommend period of 3-6 months)
data points
Improve process and/or design until reaching Pp = 2.0 and Ppk = 1.5.
Caution:
Care should be taken not to characterize a process as "ROBUST" unless the data collected includes all the sources of variation described above. One potential consequence could be the mis-allocation of tolerances on a new design. can you think of other consequences?

17. Beyond Six Sigma
Once reached, should we continue to collect SPC data and reduce variation?
IS THE JUICE WORTH THE SQUEEZE?
Economic/cost benefit.
Pareto new opportunities.
Russo, Marciano, Elephant Charts.
Scrap, rework & repair reports.
QCPC turnbacks.
Look at reducing frequency of check.
Incorporate mistake-proofing devices on key process parameters to control process.

18. Summary
The choice of using Cp & Cpk vs. Pp & Ppk is not significant if the process is in a state of statistical control.
Get the short-term variation under control.
Assess measurement system using Gage Capability Studies.
Assess machine using Machine Capability Studies or laser/ball-bar checks.
Getting long-term variation to equal the short-term variation is done by removing turnbacks through QCPC, Root cause Analysis, and Mistake-Proofing methods.
Use the right index for the appropriate bilateral or unilateral tolerance.
Reaching Six-Sigma quality levels is an excellent goal to strive for.