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The in-control performance of self-starting EWMA and X charts
Journal of the Korean Data & Information Science Society 2018;29:851-60
Published online July 31, 2018
© 2018 Korean Data and Information Science Society.

Joo Weon Lee1 · Minji Kim2 · Jaeheon Lee3

123Department of Applied Statistics, Chung-Ang University
Correspondence to: Professor, Department of Applied Statistics, Chung-Ang University, Seoul 06974, Korea. E-mail: jaeheon@cau.ac.kr
Received May 22, 2018; Revised June 26, 2018; Accepted July 2, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In monitoring a process with control charts, in-control parameters should be estimated from Phase I samples because the parameters are rarely known with certainty in practice. In general, the number of Phase I samples can often be impractically large in most applications for practitioners to be assured of having performance close to the desired performance. However, collecting the sufficiently large amount Phase I samples can be difficult in some applications. At this time, the self-starting procedure helps to monitor the process using a small amount of initial samples. This paper considers the self-starting EWMA and X charts based on the self-starting procedure used in the previous research, and evaluates the in-control perfomance of two control charts by using simulation study. The average of ARL (AARL) and the standard deviation of ARL (SDARL) are used to evaluate the in-control run length performance. From simulation results, we found that there was a significant amount of variation in the in-control performance obtained by the number of initial samples, however it was not as large as we expected.
Keywords : Average of ARL (AARL), control chart, Phase I, self-starting, standard deviation of ARL (SDARL).