The Process Capability Index

Process capability indices are an attempt to show, in a single number, whether a particular process can consistently join with the requirements made on the process by internal or external actors.  A lot has been said about how dangerous it is to use these estimates without understanding the inherent limitations of the specific index used.

In and of itself process capability is an attempt to answer the specific question of can a process reliably and consistently meet our requirements.  After the process capability has been determined, we can convert it into a gauge such as Defects Per Million Opportunities (DPMO) or sigma level.  Here is a useful tool for PPM calculations for semiconductors.  What is most important to know about all of this is that one can not calculate meaningful process capability indices if the data collected  is not reflective of a process that is in control.  The reason for this is that process capability is in its essence a prediction and one can not predict anything that is not itself stable.

How DO We Get There or Methodology

Since, as stated above, process capability is meaningless unless the process itself is stable, we must analyze the process with the aid of something called a control chart in order to prove stability.   The tools to do this for normal distributions, the capability indices are calculated as:

Cp=  (HighSpec-LowSpec)/(6xSigma)

Cpk= MIN(Cpl,Cpu),     Cpl=(-Zl/3) ,    Cpu= (-Zu/3),

Zl=(u-LowSpec/Sigma),  Zu=(HighSpec-u)/sigma