Explicit Formulas of ARL on Double Moving Average Control Chart for Monitoring Process Mean of ZIPINAR(1) Model with an Excessive Number of Zeros

Abstract

Usually, the performance of control charts are widely measured by average run length (ARL). In this paper, the derivative explicit formulas of the ARL for double moving average (DMA) control chart are proposed for monitoring the process mean of zero-inflated Poisson integer-valued autoregressive first-order (ZIPINAR(1)) model. This model is fit when there are an excessive number of zeros in the count data. The performance of the DMA control chart is compared with the results of moving average and Shewhart control charts by considering from out of control average run length (ARL1). The numerical results found that the DMA control chart performed better than other control charts in order to detect mean shift in the process. In addition, the real-world application of the DMA control chart for ZIPINAR(1) process is addressed.

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“…Maghsoodloo and Barnes 9 examined the MA control chart and analyzed its conditional average run length. Further information regarding MA control charts can be found in references 10 – 13 . Areepong 14 studied explicated formulas for the ARL on an MA control chart for monitoring the number of defective products and showed that they were easy to use, calculate, and program.…”

“…The proposed chart outperformed alternative control charts through both simulated and practical examination. For the (ZIPINAR(1)) model 13 , suggested a DMA double moving average control chart. It was more effective than other control charts at identifying statistically significant changes in the mean.…”