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A new approach to analysing non-normal quality data is proposed and demonstrated for process capability analysis. The new approach uses a new family of distributions and its allied fitting procedures to approximate an unknown source distribution, and then incorporates the fitted distribution in the relevant quality procedure. Since the new fitting routines require only low degree sample moments (second degree at most), the fitted distribution is associated with appreciably smaller mean-squared-errors (MSEws) relative to those of alternative methods (3- or 4-moment routines). New first- second- and third-generation process capability indices (PCIs) for non-normal populations, analogous to current PCIs developed for Pearsonian populations, are developed and numerically demonstrated. Sample estimators for the new PCIs are compared in terms of MSEs, via Monte Carlo simulation, to available four-moment estimators for Pearsonian populations. The new PCIs consistently yield smaller MSEs.
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