Statistical Monitoring of Multivariate Count Data From Real‐Time Particle Counters

ABSTRACT

In the pharmaceutical industry, production environments are monitored for bacterial contamination. Particle counters are increasingly investigated for real‐time monitoring of viable microorganisms using count data for different particle size intervals. Monitoring these multivariate count data is challenging because the underlying joint discrete distribution is typically unknown, may differ from well‐known discrete distributions, and may be highly heterogeneous across time. Although many control charts have been proposed for multivariate count data using different multivariate Poisson distributions (e.g., Conway–Maxwell, copula‐based, and structured multivariate Poisson), multinomial distributions ( charts, generalized charts, likelihood ratio control charts), and even multivariate normal distributions (Hotelling's chart on transformed data), they have been studied mostly for quality attributes but not for microbiological or environmental monitoring with particle counter data. Therefore, this study reviews these control charts and compares their average run length (ARL) through simulations mimicking particle counter data. The results show that most charts produce incorrect type I error rates that depend strongly on simulation settings. Only two charts, monitoring total counts using a negative binomial or normal distributions, provide consistent type I error rates while maintaining comparable detection performance. A real data case study using the BioTrak instrument supports these findings.