Abstract—A control chart is one of the effective tools in statistical process control (SPC) for improving productivity, reducing defective products and providing diagnostic information. Control charting techniques have gained increasing importance recently due to the rapid advancement in technology. Many industries tend to use control charts to monitor the quality of their products or services. The adoption of variable sample size and sampling interval (VSSI) strategy significantly improved the sensitivity of Shewhart X chart in detecting small and moderate process mean shifts, in terms of average time to signal (ATS) criterion when the process shifts are specified. However, for some scenarios in real industries, the process shift size is not set to a specific value. In this case, the expected average time to signal (EATS) can be used as a measure of performance when the process shift is unknown. The EATS of the optimal VSSI X chart is numerically evaluated based on a Markov chain approach. The findings show that the VSSI X chart prevails over the Shewhart X chart under comparison. Being able to vary the sample size and sampling interval, a practitioner will have more flexibility and better control of the process and at the same time is able to detect an out-of-control signal quicker.
Index Terms—Expected average time to signal, Markov chain, process mean, variable sample size and sampling interval.
Khaw Wah Khaw and Sin Yin Teh are with the School of Management, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia (e-mail: email@example.com, firstname.lastname@example.org).
XinYing Chew is with the School of Computer Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia (e-mail: email@example.com).
Wai Chung Yeong is with the School of Mathematical Sciences, Sunway University, Petalling Jaya, Malaysia (e-mail: firstname.lastname@example.org).
Cite: Khai Wah Khaw, XinYing Chew, Sin Yin Teh, and Wai Chung Yeong, "Optimal Variable Sample Size and Sampling Interval Control Chart for the Process Mean based on Expected Average Time to Signal," International Journal of Machine Learning and Computing vol. 9, no. 6, pp. 880-885, 2019.Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).