Synthetic c charts with known and estimated process parameters based on median run length and expected median run length

ABSTRACT

In statistical process control, the total number of nonconformities per unit of a process is monitored by using the c chart. In this study, the run length performance of the synthetic c chart with known process parameter (denoted as the KP-Syn-c chart) and the synthetic c chart with estimated process parameter (denoted as the EP-Syn-c chart) are evaluated in terms of the median run length (MRL). The results show that the sensitivity of the MRL-based EP-Syn-c chart is dependent on the number of preliminary samples used in the Phase-I analysis. Furthermore, percentiles of the run length distribution are used to provide a better understanding for the run length performance of the EP-Syn-c chart. The numerical analysis shows that the required minimum number of preliminary samples can be very large for the MRL-based EP-Syn-c chart to perform similar as the KP-Syn-c chart. An optimization procedure is suggested to compute the design parameters of the EP-Syn-c chart by minimizing the out-of-control MRL. Furthermore, the optimal design procedure of the EP-Syn-c chart is also provided through minimizing the out-of-control expected MRL for the unknown process shift size. An example is provided to illustrate the design and implementation of the MRL-based EP-Syn-c chart.

KEYWORDS:

• Estimated process parameter
• expected median run length
• synthetic c chart
• median run length

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2022.2098456

Additional information

Notes on contributors

Ming Ha Lee

Ming Ha Lee received the B.Tech. degree from Universiti Sains Malaysia, the M.Sc. degree from Universiti Putra Malaysia, and the Ph.D. degree from Universiti Sains Malaysia. She is a senior lecturer with the Faculty of Engineering, Computing and Science, Swinburne University of Technology Sarawak Campus, Malaysia.

Michael B. C. Khoo

Michael B.C. Khoo is a professor in the School of Mathematical Sciences, USM. He specializes in Statistical Quality Control. He has published numerous papers in international journals indexed in the Web of Science (WoS) database. He has also reviewed numerous papers for journals indexed in the WoS database. He is a member of the American Society for Quality.

Abdul Haq

Abdul Haq graduated (PhD) from the School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand. He is an assistant professor at the Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan. His research interest is in statistical process control.

Dennis M. L. Wong

Dennis M. L. Wong received his BEng (Hons) in electronic and communication engineering and Ph.D. in signal processing from the Department of Electrical Engineering and Electronics in University of Liverpool, Liverpool, UK. His research interests include statistical signal processing and pattern classification, machine condition monitoring, and VLSI for digital signal processing.

XinYing Chew

XinYing Chew is a senior lecturer in the School of Computer Sciences, Universiti Sains Malaysia (USM). She received his PhD from the School of Mathematical Sciences, USM. Her research interest is in statistical process control and data sciences.