Explicit Formulas of Moving Average Control Chart for Zero Modified Geometric Integer Valued Autoregressive Process

Abstract

This research presents precise formulas to calculate the average time to signal (ATS) of the moving average control chart (MA chart) for detecting changes in the autocorrelation of count data when the process has zero inflation and zero deflation. Thus, a zero-modified geometric integer value autoregressive order 1 (ZMGINAR (1)) process is a suitable geometrical alternative for autocorrelated count data with an enormous (or shortfall) number of zeros. The average time to signal is a traditional control chart performance; the mean of the observations taken before a process signal that it is beyond the control limit. The numerical results demonstrate the effectiveness of the control limit in detecting changes in the effect of inflation and deflation of zeros. The usefulness of a control chart in detecting variations in the model of the process can be illustrated by the actual data sample of count data.