Process capability evaluation for square bumps with mean shift

Process capability indices have been widely used in manufacturing industries to provide numerical measures of process potential and performance. In in-plant applications, some inevitable process mean shift may be undetected when the statistical process control charts are applied, particularly, in the bumping process for square bumps. Bothe in 2002 provided a statistical reason for considering such a shift in the process mean to accommodate the undetected mean shifts for normally distributed processes when evaluating process capability. In this paper, we consider a bumping process for square bumps in which the data can be formulated as a non-central chi-square distribution, a class of non-normal distributions. To evaluate the popular yield-based process capability C_pk more accurately, we accommodate the magnitudes of undetected mean shifts using the modified capability evaluation formula and tabulate the detection powers under various subgroup sizes and non-central chi-square parameters. Based on the modified process capability evaluation, we can provide a more reliable process capability evaluation of capability index C_pk for square bumps and make more correct decisions. For illustration purpose, a real application in a bumping factory which is located on the Science-based Industrial Park in Hsinchu, Taiwan, is presented.