Environmental Monitoring Based on a Hierarchical Poisson-Gamma Model - ASQ

Environmental Monitoring Based on a Hierarchical Poisson-Gamma Model

We establish alert and action limits for environmental monitoring programs in cleanrooms in the pharmaceutical industry. Heavily skewed count data, which exhibited both overdispersion compared to the Poisson distribution and an excess of zeroes, needed to be modelled. A hierarchical Poisson-gamma model is proposed for this purpose and compared to other models proposed in the literature, demonstrating a clear improvement in terms of fit and interpretation.

Key Words: Environmental Monitoring, Gamma Distribution, Hierarchical Models, Poisson Distribution, Sampling.

By ANTJE CHRISTENSEN, HENRIK MELGAARD and JØRGEN IWERSEN, Novo Nordisk A/S, Novo Allé, 2880 Bagsværd, Denmark

POUL THYREGOD, Informatics and Mathematical Modelling, Technical University of Denmark, 2800 Lyngby, Denmark

Introduction

IN the pharmaceutical industry, cleanrooms are maintained for production and quality control. Environmental monitoring programs are performed in such rooms to ensure and document the level of cleanliness. Authorities, including the US Food and Drug Administration (FDA) and European medical agencies, quote .xed maximum levels of microbial and particle counts to be used as alert limits and action limits (USP 24 (2000); The Rules Governing Medicinal Products in the European Union (1997)). In addition, the industry is required to set their own limits based on historical data.

Standard control charts, such as a Shewhart chart, do not apply in this situation, since the data are far from being normally distributed. The incontrol distributions are heavily skewed. Numerous counts of 0 appear in class A areas, which are the cleanest areas. Furthermore, being counts, the data are not continuous. The Poisson distribution would be a natural choice for modeling such count data, but, typically, the empirical distributions exhibit overdispersion in comparison with a fitted Poisson distribution.

In large facilities, data are abundant. Up to several tens of thousands of measurements are taken each year at different points in time and at different locations. In such cases, percentiles of the empirical distribution can be used as alert and action limits. Yet, the quality of limits derived as percentiles in the tails of the fitted distribution declines rapidly with less data. Furthermore, this approach runs the risk of including out-of-control conditions. Therefore, both for large and small facilities, a model for the data would be preferred. In the literature, the traditional approach is to model overdispersed count data using the negative binomial distribution. However, this approach does not lend itself easily to further analysis, e.g., for comparing process variation in locations that are monitored with different sample sizes. In this paper, a model is proposed which accounts for the differences in sampling time and location, and results in a satisfactory fit, superior to that of previously proposed models from the literature.

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