A Bayesian Application in Process Monitoring – Establishing Limits for Dosage Units in Early Phase Process Control

Abstract

Statistical process control is considered a key tool in manufacturing. In the pharmaceutical industry, process control is essential to ensure consistent processes that yield products with satisfactory quality. Control limits play a major role in process monitoring. The purpose of this book chapter is to present a Bayesian application in which in-process control limits are established during early (Phase I) control chart formation for uniformity of dosage units (UDU) based on weight variation. The Bayesian approach utilizes posterior predictive distributions based on noninformative and informative priors (through a power prior), and the resulting control limits are compared to those obtained from more typical approaches https://www.w3.org/1998/Math/MathML"> ( ± 3 σ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_10.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , https://www.w3.org/1998/Math/MathML"> ± 5 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_11.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> % of mean, Monte Carlo simulation). The Bayesian methods, which incorporate uncertainty in the parameter estimates, provide wider control limits than some of the typical approaches investigated and proffer a potential justification of the ad hoc https://www.w3.org/1998/Math/MathML"> ± 5 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_12.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> % of the mean approach for the data analyzed.