Shewhart control chart for monitoring the mean of Poisson mixed integer autoregressive processes via Monte Carlo simulation

Abstract

Most control charts for process monitoring assume independence among observations and that the nature of the characteristics of interest is continuous. However, these assumptions are often violated in practice, include industrial engineering applications. For integer-valued autocorrelated processes, usual control charts have a poor performance. Time-series modeling and modified control limits play a fundamental role in such circumstances. In this paper, we propose a Shewhart control chart for monitoring the mean when observations can be modeled as a first order Poisson mixed integer autoregressive model - POMINAR(1) process. The performance of the proposed approach is investigated based on in-control and out-of-control average run lengths (ARL0 and ARL1, respectively) in different scenarios. Both the determination of the control limits and the evaluation of the chart are done through computational studies using Monte Carlo simulations. Practical use of the proposed approach is illustrated with two real examples for monitoring crime data and network traffic.