Abstract
In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average run length and the standard deviation of the run length are given. Practical guidelines concerning the chart design are investigated. Extensive computations based on designs of experiments are conducted to illustrate the validity of the proposed method. Comparisons with the conventional control charting procedure are also provided. The analysis of the monthly number of drug crimes in the city of Pittsburgh is displayed to illustrate our current method of process monitoring.
Highlights
This work is motivated by an empirical analysis and process control of a monthly drug crime series, which contains excess zeros and shows clear serial dependence
As cumulative sum (CUSUM) control charts are known to be sensitive in detecting small shifts, we study the performance of the CUSUM chart for monitoring ZIGINARRC (1) process
We evaluate the ZIGINARRC (1) CUSUM chart performance basing on extensive numerical experiments and presume that the parameters in this model have already been known
Summary
This work is motivated by an empirical analysis and process control of a monthly drug crime series, which contains excess zeros (over 40%) and shows clear serial dependence (see Section 5 for more details). To solve this problem, an appropriate integer-valued model is selected, further, control charts based on this model are developed. Serial dependence among the count data have been demonstrated to arise extensively in practice, typical examples are infectious disease counts, defect counts and unemployment counts, etc These data are important indicators of the epidemic study, quality control and economics analysis, and the process monitoring is essential to detect the shifts in them.
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