, and the estimated variability of the process (expressed as a standard deviation) is
, then the process performance index is defined as:
is estimated using the sample standard deviation.
Ppk may be negative if the process mean falls outside the specification limits (because the process is producing a large proportion of defective output).
, a metric that does not account for process performance not exactly centered between the specification limits, and therefore is interpreted as what the process would be capable of achieving if it could be centered and stabilized.
Larger values of Ppk may be interpreted to indicate that a process is more capable of producing output within the specification limits, though this interpretation is controversial.
[citation needed] Strictly speaking, from a statistical standpoint, Ppk is meaningless if the process under study is not in control because one cannot reliably estimate the process underlying probability distribution, let alone parameters like
[2][disputed – discuss] Furthermore, using this metric of past process performance to predict future performance is highly suspect.
[3][disputed – discuss] From a management standpoint, when an organization is under pressure to set up a new process quickly and economically, Ppk is a convenient metric to gauge how set-up is progressing (increasing Ppk being interpreted as "the process capability is improving").
The risk is that Ppk is taken to mean a process is ready for production before all the kinks have been worked out of it.
[disputed – discuss] The indices are named differently in order to call attention to whether the process under study is believed to be in control or not.
If, after carefully monitoring the process for a while, it appears that the process is out of control and producing output unpredictably (as depicted in the run chart below), one can't meaningfully estimate its mean and standard deviation.
are estimated to be 99.61 μm and 1.84 μm, respectively, then That the process mean appears to be unstable is reflected in the relatively low values for Pp and Ppk.