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Two features of the GINAR(1) process and their impact on the run length performance of geometric control charts

Morais, M. C.

Entropy (Information Theory, Probability and Statistics - special issue on Discrete-Valued Time Series), 25 (2023), 444

The geometric first-order integer-valued autoregressive process (GINAR(1)) can be particularly useful to model relevant discrete-valued time series, namely in statistical process control. We resort to stochastic ordering to prove that the GINAR(1) process is a discrete-time Markov chain governed by a totally positive of order 2 (TP2) transition matrix. Stochastic ordering is also used to compare transition matrices referring to pairs of GINAR(1) processes with different values of the marginal mean. We assess and illustrate the implications of these two stochastic ordering results, namely on the properties of the run length of geometric charts for monitoring GINAR(1) counts.