A study on the performance of the probability-limit control charts based on the geometric and negative binomial distributions

Abstract

The Shewhart-type control chart based on the geometric distribution is widely used to monitor the number of normal events between two consecutive appearances of adverse events, but this control chart relies on the normality assumption and may thus result in unsatisfactory performance due to the high skewness of the geometric distribution. Thus, one can consider the probability-limit control chart based on the geometric distribution to correct the skewness, whereas the average run length or the false alarm rate of this control chart has been shown to be seriously biased despite of the skewness correction. In this paper, we first illustrate that the biased issue is mainly due to discreteness of the geometric distribution and then advocate the use of the control chart based on the negative binomial distribution. Numerical results from extensive Monte Carlo simulations clearly show that the control chart based on the negative binomial not only reduces the bias, but also outperforms the one based on the geometric control chart in a sense of smaller bias and high alarm rate.