ESTIMATION OF MULTIVARIATE PROCESS YIELD INDEX STpk​​ FOR VARIOUS NON-NORMAL DISTRIBUTIONS USING ANN AND BURR XII DISTRIBUTION

Abstract

Process capability indices have been used in manufacturing industry to evaluate the ability of processes to meet consumer’s expectations. Traditionally, frequently used univariate and multivariate capability indices rely over the assumption of normality and multivariate normality respectively. Practically the underlying process distribution is not always univariate and normal. This gives rise to define capability indices for multivariate processes under non-normal scenario. Several multivariate process capability indices have been defined so far based on normality and non-normality. Among multivariate process capability indices based on normality,  is a multivariate overall yield index that needs normality of each independent quality characteristic. This paper chooses  and utilizes artificial neural network (ANN) and the Burr XII distribution approach to estimate  under multivariate non-normal situations. The method was applied to the data sets under non-normal scenarios. The estimates obtained from proposed method were compared with the results of existing traditional indices under normality by translating the non-normal data sets to normality using suitable transformations. The results suggest that the proposed method successfully estimates  under multivariate non-normal environments.