00105 �03ace3403aee62d22aac93e4bd4d18

Economic Control Charts: Relating the Model and Finding the Optimal Design

Thomas P. McWilliams Arizona State University West Phoenix, Arizona

Abstract

The practitioner wishing to implement an economic or economic statistical control chart design is faced with a variety of models which have appeared in the ąuality control literaturę. These models vary according to the type of chart considered, assumptions madę regarding process behavior, and the notation used. In an attempt to clarify the situation, I present and discuss the relationship between eleven earlier np- and X -chart models and the unified Lorenzen-Vance model. In addition, I develop an accurate approximation for the time between samples which facilitates quick calculation of optimal control chart parameters.

Introduction

A considerable number of articles dealing with economic control chart models can be found in the ąuality control literaturę, beginning with Duncan's 1956 economic X -chart article. In the economic approach, control chart

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