Synthetic c charts with known and estimated process parameters based on median run length and expected median run length. Issue 2 (4th March 2023) - Lee, Ming Ha; Khoo, Michael B. C.; Haq, Abdul; Wong, Dennis M. L.; Chew, XinYing
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.