On the one-chart schemes for joint monitoring of the two parameters of a zero-inflated Poisson (ZIP) process

Abstract

One-chart scheme for joint monitoring of two parameters allows the practitioners to focus on a single chart and thus, it offers significant  operational advantages. Recently, four one-chart schemes are reported in literature for joint monitoring of the two parameters (, ) of a  zero-inflated Poisson (ZIP) process. One of these schemes, namely - Gamma chart, is developed assuming samples of large size will be  inspected and other three charts, namely DS-chart, Max-chart and LR chart, are developed assuming samples of small size will be  inspected after every certain interval. The plotting statistics of these three charts are computed using the estimated ZIP parameters.  However, unless the sample size () is sufficiently large, the excessive number of zeros in the ZIP process may offer a sample of zeros only.  Therefore, these three schemes require estimation of ZIP parameters and subsequent computation of the plotting statistic based on the  accumulated samples till the sampling stage. Because of the accumulation of samples, these schemes suffer from several limitations. In  this paper, these one-chart schemes are modified for large sample size to make them free from their limitations. Subsequently, the  performances of the four one-chart schemes are evaluated extensively using simulation studies. The results reveal that among the three  modified charts likelihood ratio (LR) chart is the most preferable with respect to in-control and out-of-control average run length (ARL)  performances. However, all these three modified charts give false alarms when the process parameter(s) shift towards desirable  direction(s) implying process improvement. On the other hand, the Gamma chart is slightly inferior with respect to out-of-control ARL  performances. But it does not give false alarm when there is a process improvement. Further, since Gamma chart directly monitors the  average number of defects, it offers significant advantages in terms of implementation and interpretations.