Process Capability and Performance Indicators (Pp, Ppk, Cp, Cpk)

Process Capability & Performance Indicators (Pp, Ppk, Cp, Cpk) are specification indicators relative to process dispersion and process centering.

 

Process capability is a statistical measurement of a process’s ability to produce parts within specified limits consistently, to meet the design specification for a service or a product.

 

Process capability is expressed as 6σ, where σ is the sample standard deviation of the process under a state of statistical control.

 

Process capability refers to the inherent ability of a process to produce similar parts for a sustained time under a given set of conditions.

 

A capable process is one where almost all the measurements fall inside the specification limit whose spread on the bell-shaped curve is narrower than the tolerance range.

 

• Process Performance Indicators (Pp, Ppk)
• Process Capability Indicators (Cp, Cpk)
• Z score and process capability

 

Cp, Cpk, Pp, and Ppk measure how close our process is running to its specification limits.

 

For requirements, we measure the process specifications. To determine the answers, we see how wide the process dispersion is and how centered the process is relative to those specifications.

 

Note: use Pp & Ppk when you are initially setting up your process. After a process has reached statistical control, use Cp & Cpk.

 

Let’s imagine that your process has 2 specifications; a Lower Specification Limit (LSL) which is the lowest value allowed, and an Upper Specification Limit (USL), the highest value allowed.

 

We call the difference between the two the specification spread, sometimes referred to as the Voice of the Client.

 

The process spread is the distance between the highest value generated and the lowest. We sometimes refer to this as the Voice of the Process.

 

Can A Process Meet Specifications?

If your process spread exceeds the specification spread, then the answer is no.

However, if the process spread is less than the specification spread, then process variation is low enough for it to fit.

 

Pp = (USL – LSL) / 6 * s = 12 σ / 6 * s = 2 σ / s

 

s: standard deviation

 

According to Six Sigma, we want a Pp of above 1.5 because that would reflect a process with less than 3.4 DPMO – the definition of 6 Sigma quality.

 

USL – LSL should = 12

 

Is the Process Acceptable? Ppk (Capability)

 

Ppk is another performance index that measures how close the current process means proximity is to the specification limits.

 

A Ppk of 1 means that there is “half of a bell curve” between the center of the process and the nearest specification limit. That means your process is completely centered.

 

Ppk can be determined by dividing the Z score by three.

A z score is the same as a standard score; the number of standard deviations above the mean.

 

z= (x – µ)/σ

Z = x – mean of the population / standard deviation.

 

Ppk = ( USL – µ) / 3σ = z / 3

 

Read also: Process Validation in Pharmaceutical Industry