Exponentially Weighted Moving Average Hypergeometric <i>np</i> Control Scheme

Control schemes are often used to monitor variables, but not all process data fit this description, as some data may actually be attributive in nature. For this reason, considerable attention has recently been paid to control schemes designed for attributes. In particular, new control schemes based on the hypergeometric distribution, namely hypergeometric p and np schemes, have been proposed. However, these schemes are mostly Shewhart-type control schemes, and they are often criticized due to their inferior performance in detecting small and medium shifts. To address this issue, we present the exponentially weighted moving average (EWMA) hypergeometric np scheme in this paper. Similar to the hypergeometric np scheme, the proposed scheme is more practically convenient than the hypergeometric p scheme since it works with integer values. Since computing the run length properties for an EWMA scheme that depends on discrete data is challenging, we also consider the continuousify technique in this paper. We compare the introduced scheme with the existing hypergeometric np control scheme and demonstrate that the former scheme outperforms the latter scheme for all shift sizes. Furthermore, we investigate the optimal design of the EWMA hypergeometric np scheme to enhance its practicality and illustrate its application on a real dataset.