Evaluating process capability under undetected fluctuations

Process capability indices (PCIs) have been widely applied to provide numerical measures of process potential and performance in high technology processes requiring very low fraction of nonconformities. Since capability indices are alternatives for measuring manufacturing yield and the key factors for the evaluation of outsourcing suppliers, an accurate and stringent evaluation of the process capability is very essential. In manufacturing processes, some inevitable process fluctuations may be undetected when the statistical process control charts are applied. Bothe [Bothe, D. R., 2002. Statistical reason for the 1.5-sigma shift. Quality Engineering 14(3), 479-487] 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. Existing research works have reported the capability modifications which only cover either undetected mean shift or undetected variance change. In this paper, to assess the popular yield-based process capability index C_pk more accurately, we accommodate the magnitudes of undetected mean shift and variance change simultaneously using a modified capability evaluation formula. For illustration purpose, a case in real-world application is presented.