Properties and performance of one-sided cumulative count of conforming chart with parameter estimation in high-quality processes

The one-sided cumulative count of conforming (CCC) chart is a useful method to monitor nonconforming fraction in high-quality manufacturing processes. The nonconforming fraction parameter is assumed to be known when implementing a one-sided CCC chart. In this study, we investigated the impact of estimated nonconforming fraction, <italic>[pcirc]</italic> ₀, in a one-sided CCC chart. The run length distribution is derived as well as the conditional probability of a false alarm rate (CFAR), conditional average run length (CARL) and its standard deviation (CSDRL). Simulation results are conducted to evaluate the effect of <italic>[pcirc]</italic> ₀ in a one-sided CCC chart. The results show that values of CFAR, CARL and CSDRL are close to the nominal values for a large sample. The impact of estimation errors was also studied. We find that CFAR decreases for large <italic>[pcirc]</italic> ₀. Thus, a large value of <italic>[pcirc]</italic> ₀ is suggested for fewer false alarms.