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

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.