Control charts to monitor integer valued autoregressive process with inflation or deflation of zeros

Abstract

In this paper, we call attention for monitoring autocorrelated count data when there is an excessive (or deficit) number of zeros in the count data. In particular, we propose to control the autocorrelated count data based on a zero-modified geometric INAR(1) process, which is an alternative to the geometric one, for monitoring autocorrelated counts with an excessive (or deficit) number of zeros. Numerical results are provided regarding the performance of the considered charts in the detection of changes in the mean of the process as well as the effects of zero-inflation and zero-deflation are provided. The usefulness of the considered model is illustrated via two real-data examples in challenging cases of deflated and inflated count data.

Subject Classification:

• 62H10
• 46N30
• 97K80

Keywords:

• Average run length
• CUSUM chart
• INAR(1) process
• Integer-valued time series
• Zero-modified geometric distribution