Optimal design of the side sensitive group runs double sampling (SSGRDS) X ¯ scheme with estimated process parameters

The side sensitive group runs double sampling (SSGRDS) X ¯ scheme is previously studied under the known process parameters (Case-K) assumption. As the process parameters are hardly known in practical situations, they must be estimated using a suitably chosen in-control (IC) Phase-I sample. However, various studies demonstrated that a substantial amount of Phase-I sample is necessary so that the scheme with unknown process parameters (Case-U) attains a performance almost similar to that of the Case-K counterpart. Since it is challenging to acquire a vast number of IC samples, we examine the optimal designs of the Case-U SSGRDS X ¯ scheme such that the average number of observations to signal (ANOS) and expected ANOS (EANOS) are minimised. The optimal parameters obtained for the Case-U SSGRDS X ¯ scheme enable it to have a performance comparable to that of the Case-K counterpart, without the need for a large number of Phase-I samples. We show that the Case-U SSGRDS X ¯ scheme is effective in identifying the process mean shift of a silicon epitaxial process.