TL;DR: The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered and multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches.
Abstract: The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.
TL;DR: The purpose of this paper is to exposit a control chart technique that may be of value to both manufacturing and continuous process quality control engineers: the exponentially weighted moving average (EWMA) control chart.
Abstract: The Shewhart and CUSUM control chart techniques have found wide application in the manufacturing industries. However, workpiece quality has also been greatly enhanced by rapid and precise individual item measurements and by improvements in automatic dynamic machine control. One consequence is a growing similarity in the control problems faced by the workpiece quality control engineer and his compatriot in the continuous process industries. The purpose of this paper is to exposit a control chart technique that may be of value to both manufacturing and continuous process quality control engineers: the exponentially weighted moving average (EWMA) control chart. The EWMA has its origins in the early work of econometricians, and although its use in quality control has been recognized, it remains a largely neglected tool. The EWMA chart is easy to plot, easy to interpret, and its control limits are easy to obtain. Further, the EWMA leads naturally to an empirical dynamic control equation.
TL;DR: A criterion that measures approximately the average net income of a process under surveillance of an X chart when the process is subject to random shifts in the process mean is established.
Abstract: This paper establishes a criterion that measures approximately the average net income of a process under surveillance of an X chart when the process is subject to random shifts in the process mean. The quality control rule assumed is that an assignable cause is looked for whenever a point falls outside the control limits. The criterion is for the case in which it is assumed that the process is not shut down while the search for the assignable cause is in progress, nor is the cost of adjustment or repair and the cost of bringing the process back into a state of control after the assignable cause is discovered charged to the control chart program. The paper shows how to determine the sample size, the interval between samples, and the control limits that will yield approximately maximum average net income. Numerical examples of optimum design are studied to see how variation in the various risk and cost factors affects the optimum. * The writer is greatly indebted to I. R. Savage and G. Greggory of ...
TL;DR: In this article, the control chart limits are calculated using parameter estimates from an in-control Phase I reference sample, and statistics based on new samples are compared with the estimated control limits to monitor for departures from the in..
Abstract: Control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II monitoring, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in..
TL;DR: Control limits for both types of contributions are introduced to show the relative importance of a contribution compared to the contributions of the corresponding process variables in the batches obtained under normal operating conditions.