Calculating the Process Capability Ratio for Weibull Data

Abstract

     The process capability ratio is one of many statistical process control widely used in manufacturing and service engineering based on normality assumption. If the data do not correspond with the assumption, they can lead to erroneous conclusions. So the wrong conclusions would cost manufacturing and service organization big financial losses and lost customers to competitors. One approach to dealing with this situation is to transform the data so that in the new, the transformed data have a normal distribution appearance. Many authors investigated the standard transformation such as square root, logarithmic, and so on including the well known Box-Cox transformation to transform data are not normally distributed to normality. However, transformations may behave sufficiently normal for statistical process control but they do not yield accurate process performance index.  In this paper, the use of Manly transformation, Yeo-Johnson transformation, and Nelson transformation to transform Weibull data are investigated in sense of calculating the process capability ratio and the coefficient of variation. It is found that all of three transformations can be used for transforming Weibull data to data that are normally distributed and the average of the process capability ratio of transformed data via all of them is not different at significant level 0.05 although the average of coefficient of variation of data transformed by Nelson transformation is the lowest. However, Nelson transformation is easy to work because it does not need the transformation parameter.