1. Process Capability

2. Process Capability
The natural variation of a process should be small enough to produce products that meet the standards required
A process in statistical control does not necessarily meet the design specifications
Process capability is a measure of the relationship between the natural variation of the process and the design specifications

3. Process Capability Ratio
Cp =
Upper Tolerance Limit (UTL) - Lower Tolerance Limit (LTL) 6s
A capable process must have a Cp of at least 1.0
Does not look at how well the process is centered in the specification range
Often a target value of Cp = 1.33 is used to allow for off-center processes
Six Sigma quality requires a Cp = 2.0

4. Process Capability Ratio
In GE insurance claims process, Process mean x = minutes and the process standard deviation is minutes. The design specification to meet customer satisfaction is 210 ± 3 minutes. So the upper specification (the Upper Tolerance Limit) is 213 minutes and the lower specification (the Lower Tolerance Limit) is 207 minutes. The manager wants to compute the process capability ratio.
Cp =
UTL - LTL 6s
=1.938
6(.516)
Cp =

5. Process Capability Ratio

6. Process Capability Index
The simple Cp measure assumes that the average of the process variation is at the midpoint of the specification range. Often the process average is offset from the specification range. In such cases, one-sided capability indices are required to understand the capability of the process
Upper one-sided index Cpu =
Lower one-sided index Cpl =

7. Process Capability Index
Sometimes only the lower of the two one-sided indices for a process is used to indicate its
capability (Cpk):
Cpk = min( Cpu , Cpl )
A capable process must have a Cpk of at least 1.0
A capable process is not necessarily in the center of the specification, but it falls within the specification limit at both extremes

8. Process Capability Index
In a process of filling boxes of rice where we measure the weight of each box, the process average is 210 g and the specification range is between 198 g and 214 g and the standard deviation of the process is 2 g. Calculate the Process Capability Index.
The process is not capable and therefore cannot meet specifications

9. Process Capability Index
You are the process improvement manager and have developed a new machine to cut insoles for the company’s top-of-the-line running shoes. You are excited because the company’s goal is no more than 3.4 defects per million and this machine may be the innovation you need. The insoles cannot be more than + or – of an inch from the required thickness. You want to know if you should replace the existing machine, which has a Cpk of 1.0
New process mean x = .250 inches
Process standard deviation = inches
Upper Specification Limit = .251 inches
Lower Specification Limit = .249 inches

10. Process Capability Index
New process mean x = .250 inches
Process standard deviation = inches
Upper Specification Limit = .251 inches
Lower Specification Limit = .249 inches
Cpk = minimum of ,
(.251)
(3).0005
(.249)
Both calculations result in
New machine is NOT capable
Cpk = = 0.67
.001
.0015

11. Interpreting Cpk Cpk = negative number Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
LTL UTL