Effect Of Parameter Estimation On The Performance Of Control Charts Based On Geometric Distribution

A high-quality process,ranging from production of microelectronics to surveillance systems used for healthcare,is always associated with a low nonconforming rate.It is of vital importance to use a proper control chart to effectively monitor the process with a low nonconforming rate.The parameters of the phase I process are rarely known.Thus,a considerably large sample size is needed to accurately estimate nonconforming rate and we also need to know the effects of parameter estimation on the performance of control charts.Firstly,CCC-r charts are charts based on Geometric data can be used for a low nonconforming rate process.Parameters for the charts are defined by using Bayesian method and binary method.By comparing the in-control and out-of-control performance,we recommend the use of the CCC-4 chart as a better choice for its stability to parameter estimation as well as its effectiveness in detecting shifts.Furthermore,comparison has been made among CCC-4 chart,Geometric CUSUM chart and Synthetic chart.We use Bayesian method as well as Markov method to define parameters for Geometric CUSUM chart and Synthetic chart.It is investigated that the CCC-4 chart is less sensitive to parameter estimation while being more effective in detecting different process shifts when compared with Geometric CUSUM chart and Synthetic chart.Finally,an example is given to show the effectiveness of CCC-4 chart.When considering the stability of chart to parameter estimation,easier construction in practice as well as the effectiveness in detecting shifts,we recommend the use of CCC-4 chart.