It is possible to analyze non-normal data when conducting a capability analysis – even if it cannot be transformed to a state of normality.  Of course, this position assumes that the underlying distribution is unimodal in nature (i.e., not multimodal).  Technical details aside, this particular type of problem can quickly become an analytical nightmare for the novice practitioner.  Consequently, your resident statistician should be consulted before taking any type of definitive action.

Upon the advise of a statistician, it may be found that nonparametric statistics can be applied to resolve the problem.  By design, such statistics do not make an assumption about the distribution’s shape.  If the application of nonparametrics is not possible or convienent, try downgrading the natural scale of measure.

To illustrate this option, let us consider a unimodal distribution that is severely skewed – to such an extent that it cannot be transformed to fit any type of classic distribution.  Given this, all is not lost.  If the scale of measure can be forced from its continuous form (ratio or interval scale) to a discrete base (nominal scale), it might then be possible to assign a Sigma value – thereby, providing a measure of equivalent capability.

For example, consider the instance where the Defects-Per-Million-Opportunites is given as DPMO = 3.4.  With this metric in hand, we can readily establish the equivalent long-term Z by way of a conversion table.  Doing so would reveal Z.lt = 4.5s.  Of course, such a long-term “Sigma value” can be presented in its short-term form by the simple addition of 1.5s.  Thus, a short-term Z of 6.0 corresponds to an equivalent long-term quality level of 3.4 DPMO.