One-Sided EWMA Control Chart For Auto-correlated Process Of Count Data And Performance Analysis

This paper considers one-sided EWMA control chart for auto-correlatedprocess of count data. Based on floor and ceil rounding function, one-sidedAF-EWMA and AC-EWMA control charts are built to monitor first-orderinter-valued auto-correlated process with Poisson count data. BivariateMarkov chain model is used to calculate the average run length of these charts.On the basis of ARL values, performance of the control charts is analyzed andcompared. For detecting positive shifts of the mean, it is shown that theperformance of AF-EWMA chart is better than that of AC-EWMA andAR-EWMA charts. Besides, AF-EWMA chart is robust to the change ofcontrol chart starting value.For the control chart of process with auto-correlated count data, it iscommon to assume that the INAR(1) process parameters are known or can beaccurately estimated. However, in practice, the in-control process mean andautocorrelation coefficient are typically unknown and must be estimated. Inthis article, we investigate the effect of parameter estimation on the run lengthproperties of Poisson INAR(1) one-sided AF-EWMA chart with the use ofbivariate Markov chain approach. It is shown from the conditional in-controland out-of-control ARL values with different design parameter under variousshift magnitudes that the effect of parameter estimation error can besignificant. Meanwhile, the effect due to the process mean estimation error isstronger than that due to the autocorrelation coefficient. We also providesample size recommendation regarding marginal performance. This samplesize depends on the different shift magnitudes.