Process capability estimation for non-normal quality charactersitics using Clement, Burr and Box--Cox methods

Shafiq Ahmad, Malihe Abdollahian, Panlop Zeephongsekul


In today's competitive business environment, it is becoming more crucial than ever to assess precisely process losses due to non-compliance to customer specifications. To assess these losses, industry is widely using process capability indices for performance evaluation of their processes. Determination of the performance capability of a stable process using the standard process capability indices requires that the underlying process data should follow a normal distribution. However, if the data is non-normal, measuring process capability using conventional methods can lead to erroneous results. Different process capability indices such as Clements percentile method and data transformation method have been proposed to deal with the non-normal situation. Although these methods are practiced in industry, there is insufficient literature to assess the accuracy of these methods under mild and severe departures from normality. This article reviews the performances of the Clements non--normal percentile method, the Burr based percentile method and Box--Cox method for non-normal cases. A simulation study using Weibull, Gamma and lognormal distributions is conducted. Burr's method calculates process capability indices for each set of simulated data. These results are then compared with the capability indices obtained using Clements and Box--Cox methods. Finally, a case study based on real world data is presented.


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.