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

The side sensitive group runs double sampling (SSGRDS) x̄ 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 x̄ 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 x̄ 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 x̄ scheme is effective in identifying the process mean shift of a silicon epitaxial process.