Control charts based on dependent count data with deflation or inflation of zeros

ABSTRACT

The process of serially dependent counts with deflation or inflation of zeros is commonly observed in many applications. This paper investigates the monitoring of such a process, the first-order zero-modified geometric integer-valued autoregressive process (ZMGINAR(1)). In particular, two control charts, the upper-sided and lower-sided CUSUM charts, are developed to detect the shifts in the mean process of the ZMGINAR(1). Both the average run length performance and the standard deviation of the run length performance of these two charts are investigated by using Markov chain approaches. Also, an extensive simulation is conducted to assess the effectiveness or performance of the charts, and the presented methods are applied to two sets of real data arising from a study on the drug use.

KEYWORDS:

• Cumulative control chart
• forecasting
• integer-valued autoregressive process
• statistical process control
• zero-modified distribution

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Dehui Wang  http://orcid.org/0000-0002-9185-9034

Additional information

Funding

This work is supported by China Scholarship Council, National Natural Science Foundation of China under grant numbers [11501241, 11571051, 11631003, 11690012, 11731015, 11871028]; Natural Science Foundation of Jilin Province under grant numbers [20150520053JH, 20170101057JC, 20180101216JC]; Program for Changbaishan Scholars of Jilin Province under grant number [2015010].