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3

Introduction

is usually neglected in textbooks.

Section II contains three papers focusing on economic models of control charts. This topie has received considerable attention in the statistics, engineering, and operations research literaturę over the last 40 years, because it combines elegant mathematical modeling concepts with reasonably complex optimization issues. The first and third paper in this section are by T. P. Mc Williams. The first paper unifies much of the literaturę in this field by relating eleven different economic models for Shewhart control charts to the well-known Lorenzen-Vance model. He also presents an accurate approximation for the time between samples which facilitates simple determination of the optimal control limits. The third paper adds a "cyclic duration constraint" to the Lorenzen-Vance economic model that consists of an upper bound on the 95th percentile of the out-of-control run length distribution. This constraint is shown to be very effective in ensuring that the probability of an extremely long run length when the process is out of control is smali. The paper contains an extensive collection of previously published examples.

The second of the three papers in the section, entitled "Optimization and Sensitivity Analysis with an Economic Control Chart Model Using the CUSUM," is co-authored by J. R. Simpson and J. B. Keats. They show that only a few of the 12 cost and system parameters in the Lorenzen-Vance model are really critical to the optimal solution. The authors also investigate unconstrained optimization of the cost function followed by a trade-off analysis in the region of the optimum as an altemative to constrained optimization in an effort to find economically effective Solutions with good statistical properties. This approach produces excellent results. This paper should be of significant value to anyone who wishes to implement economic control chart designs in practice.

Section III presents three papers on the integration of statistical process control (or SPC) and engineering process control (or EPC). This can also be viewed as the combination of statistical monitoring with a process adjustment techniąue. Process adjustment methods have been used successfully for decades, usually in the process industries, to make compensating adjustments in some manipulatable variable to counteract the effects of disturbances in an input stream on some process output. SPC methods, in contrast, have arisen and traditionally been applied in the discrete parts industries. In this setting, process adjustments are only madę following an action signal on a control chart. The statistical framework of EPC is parameter estimation, while the statistical framework of SPC is hypothesis testing. In recent years, many authors have noted that both methods have as their objective the reduction of process variability, and so combination or