Synthetic c charts with known and estimated process parameters based on median run length and expected median run length. Issue 2 (4th March 2023)

• Record Type: Journal Article
• Authors: Lee, Ming Ha; Khoo, Michael B. C.; Haq, Abdul; Wong, Dennis M. L.; Chew, XinYing
• Is Part Of: Quality technology & quantitative management. Volume 20:Issue 2(2023)
• Page Start: 168
• Page End: 183
• Publication Date: 2023-03-04
• Subjects: Estimated process parameter -- expected median run length -- synthetic c chart -- median run length; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2022.2098456
• Languages: English
• ISSNs: 1684-3703

Abstract

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.