The Poisson INAR(1) one-sided EWMA chart with estimated parameters

Abstract

The Poisson INAR(1) one-sided exponentially weighted moving average (EWMA) chart has been proposed to monitor integer-valued autoregressive processes of order 1 with a Poisson marginal distribution. It is common to assume that the INAR(1) process parameters are known or can be accurately estimated. However, in practice, the in-control process mean and autocorrelation coefficient are typically unknown and must be estimated. In this article, we investigate the effect of parameter estimation on the run length properties of the Poisson INAR(1) one-sided EWMA chart with the use of bivariate Markov chain approach. It is shown from the conditional in-control and out-of-control average run length values with different design parameters under various shift magnitudes that the effect of parameter estimation error can be significant. The effect due to the process mean estimation error is stronger than that due to the autocorrelation coefficient. Moreover, practitioners should rarely expect the in-control performance to be close to that obtained under the assumption that process parameters are known. We also provide sample size-recommendations regarding marginal performance. This sample size depends on the different shift magnitudes.

Keywords:

• Poisson process
• auto-correlated count process
• AF-EWMA control chart
• estimation error

Acknowledgements

The authors thank Professor William H. Woodall of Virginia Tech (USA) for his valuable comments that led to significant improvements to this article.

Funding

This research was supported by [grant number 71225006], [grant number 71002105] from the National Natural Science Foundation of China.