Interaction between capability indices and skewness of nonnormal processes using quantile based estimation and Johnson transformation

Many process capability indices have been developed for non-normal process but there has been little research about the skewness nowadays. The aim of this research work is to investigate the interaction between capability indices and skewness by using three estimation methods like conventional, Johnson transformation, and quantile based methods to take into consideration symmetrical and non-symmetrical parameter of different kind of distributions such as gamma- and skew t-distribution. To demonstrate the interaction between skewness and process capability indices Cp, and Cpk, the random data of size 100 for data sets of gamma- and skew t-distribution for skewness ranging from 0.5, 1.0, 1.5, 1.8 to 2.0 has been generated by using of MINITAB15. Obviously, it is seen that for the skewness parameters of the different distributions, estimation of both the gamma- and skew tdistribution by calculating three techniques are decreasing after the "skewness parameter 1.8". Furthermore, the main findings indicated that the skewness of the distributions have a significant influence on the methods to compute the process capability indices, therefore on the improvement of the manufacturing process, respectively.