Setting Alert and Action Limits in the Presence of Significant Amount of Censoring in Data

Abstract

In manufacturing settings, control limits are often set using a three-sigma rule (i.e., three estimated standard deviations above and below the estimated mean). More sophisticated statistical methods might include the use of confidence, prediction, or tolerance intervals. However, in environmental monitoring of microbial excursions in aseptic manufacturing operations, most of the assayed measurements fall below the limit of quantitation. In such circumstances, it is inappropriate to directly calculate control limits with a mean plus two or three standard deviations to represent the center and spread of the data. The system under consideration assumes that microbial assayed values stem from a log-normal distribution with two sources of variability to account for testing occasions and measurements made within a testing occasion. Bayesian statistical methods and a Tobit likelihood are used to model the observed and left-censored data in order to predict the distribution of new data. Control limits are generated from quantiles of the posterior predictive distribution.

LAY ABSTRACT: In manufacturing settings, control limits are used to ensure either the manufacturing process or environment is in a state of control. These limits can be set using a three-sigma rule (i.e., three estimated standard deviations above and below the estimated mean) or via more sophisticated statistical methods. In this paper, we consider setting the control limits for a clean room setting in which microbial excursions are rare. Under such circumstance, the measurements of microbial counts are often below the limit of quantification. We develop methods based on Bayesian analysis and a Tobit regression to more accurately estimate control limits.