Mary G. Leitnaker

A Statistical Process Control Framework for the Characterization of Variation in Batch Profiles

An statistical process control framework for the characterization of the systematic variability in a historical database of batch profiles is proposed. The framework is geared toward facilitating an understanding of the sources of variability affecting the process. The overall variability in the profiles is categorized into two parts, systematic and unsystematic. The former is further divided, as along the time axis and the measurement axis. Scaling methods are applied to the profiles to obtain scale parameters that characterize the systematic time and measurement axis variability. The profile scaling is proposed so that each parameter has a very specific meaning in terms of the type of variability explained. Multivariate SPC charts on the scale parameters and also on the residuals remaining after scaling are developed for process monitoring. Profiles from two simulation examples, a simulated methyl methacralate polymerization reactor and a nylon-6,6 reactor, are used to demonstrate the application of the SPC framework. The examples demonstrate that a systematic study of the correlation structure of the scale parameters can reveal the signature of the primary disturbances affecting the process. Besides providing meaningful scale parameters, the framework also retains the power of projection methods for subtle special cause detection. The demonstration also highlights the importance of using the time variability information for final product quality predictions in batch data mining.

THE ANALYTIC EXAMINATION OF TIME-DEPENDENT VARIANCE COMPONENTS

Dr. Deming states that the application of statistical theory to enumerative problems is generally correct, but the application of traditional techniques to analytic problems may be misleading. An example is the use of traditional nested designs to stud..

Using Statistical Thinking and Designed Experiments to Understand Process Operation

ABSTRACT Using a series of four case studies, this article illustrates the integration of statistical process control and designed experiments. For such an integration to be effective, this article points out the need to use statistical process control (SPC) as a tool for active process study, rather than simply as a method for maintaining and controlling processes. The use of SPC in this fashion is also illustrated throughout the case studies.

Randomized Complete Block Designs in Industrial Studies

The use of randomized complete block designs is considered as a proactive method for collecting data to develop further understanding of the sources of variation affecting process outputs. The purpose of the randomized block design has traditionall..

Online batch recipe adjustments for product quality control using empirical models: Application to a nylon-6,6 process

The application of batch profile characterization tools to enhance process understanding by uncovering the signature of the primary disturbances on the profiles and its effect on the product quality is illustrated on a nylon-6,6 process. The historical profile data for the fixed recipe operation are systematically studied to understand the primary disturbances affecting the process, and it is shown that good online predictions of the final product quality are possible much before the completion of the batch from the available measurement profiles. A simple online recipe adjustment strategy based on the predicted quality deviation from the target is proposed. Results show that the recipe adjustments significantly reduce the variation in the final product quality. Issues in the use of empirical prediction models from recipe-based data are discussed.

Analytic Use of Two-Level Factorials in Incomplete Blocks to Examine the Stability of Factor Effects

Incomplete block designs are used in industry to analyze the consistency of factor effects across blocks are summarized. Correct analyses of these designs are described...

Non-linear compartmental systems: extensions of S. R. Bernard's urn model

One of the limitations of stochastic, linear compartmental systems is the small degree of variability in the contents of compartments. S. R. Bernards (1981) urn model (S. R. Bernardet al., Bull. math. Biol. 43, 33–45.) which allows for bulk arrivals and departures from a one-compartment system, was suggested as a way of increasing content variability. In this paper, we show how the probability distribution of the contents of an urn model may be simply derived by studying an appropriate set of exchangeable random variables. In addition, we show how further increases in variability may be modeled by allowing the size of arrivals and departures to be random.