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 Cpk 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 Cpk 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.
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