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

Author:

Chong Zhi Lin1ORCID,Yeong Wai Chung2,Khaw Khai Wah3,Chew XinYing4,Teoh Wei Lin5ORCID

Affiliation:

1. Department of Electronic Engineering, Faculty of Engineering and Green Technology, Universiti Tunku Abdul Rahman, Malaysia

2. School of Mathematical Sciences, Sunway University, Malaysia

3. School of Management, Universiti Sains Malaysia, Malaysia

4. School of Computer Sciences, Universiti Sains Malaysia, Malaysia

5. School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Malaysia

Abstract

The side sensitive group runs double sampling (SSGRDS) [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] scheme is effective in identifying the process mean shift of a silicon epitaxial process.

Funder

Universiti Tunku Abdul Rahman Research Fund

Publisher

SAGE Publications

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