Process Capability

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

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

Process Capability Ratio

Cp = UTL - LTL

6s

In GE insurance claims process, Process mean x = 210.0 minutes and the process standard deviation is 0.516 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 = =1.938213 - 2076(.516)

Process Capability Ratio

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 =

3

XUTL

3

LTLX

Process Capability Index

Sometimes only the lower of the two one-sided indices for a process is used to indicate itscapability (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

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

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 – 0.001 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 inchesProcess standard deviation = .0005 inchesUpper Specification Limit = .251 inchesLower Specification Limit = .249 inches

Process Capability Index

Cpk = = 0.67.001.0015

New machine is NOT capable

Cpk = minimum of, .)251. - (250

)3.(0005

.250.) - 249()3.(0005

Both calculations result in

New process mean x = .250 inchesProcess standard deviation = .0005 inchesUpper Specification Limit = .251 inchesLower Specification Limit = .249 inches

Interpreting Cpk

Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1

LTL UTL