Two Features of the GINAR(1) Process and Their Impact on the Run-Length Performance of Geometric Control Charts

Autor:	Manuel Cabral Morais
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	discrete-time Markov chain TP2 transition probability matrix Kalmykov order statistical process control run length Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 25, Iss 3, p 444 (2023)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e25030444
Popis:	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 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.
Databáze:	Directory of Open Access Journals
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