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Simpson & Keats

by a trade-off analysis in the region of optimality. Results here suggest that unconstrained optimization followed by trade-off analysis offers morę benefits and avoids critical errors relative to constrained optimization. We conclude with a economic comparison of the X and CUSUM procedures using the LV model and these results indicate that the CUSUM procedurę compares favorably with the X, for a wide rangę of cases, even with larger shifts in the process mean.

Introduction

The purpose of implementing statistical process control (SPC) techniąues is to improve the ąuality of the product by reducing variability in the process. A company that produces from a process that is stable or repeatable will benefit from increased customer satisfaction, enhanced productivity, and reduced costs. Statistical Process Control most often takes the form of graphical, charting procedures or their analytical equivalents. Different control chart types possess different performance ąualities. In fact, we might classify control chart applications to be of three types: those primarily designed to identily larger shifts (in excess of one process standard deviation), those designed to detect smaller shifts, and those that must identify both large and smali shifts. The X and Cumulative Sum (CUSUM) charts are the most widely used SPC procedures for monitoring variables in production processes. The X chart for variables has been used extensively sińce its introduction by Walter Shewhart (1925). The CUSUM, based on procedures developed by Page (1954), is receiving increased emphasis in industry due to the popularity of an analytical version of the chart.

X and CUSUM procedures are usually compared with respect to statistical properties. Statistical performance indicates the degree to which the chart is expected to provide quick detection of true assignable causes. Assignable causes are identified by shifts or drifts in the process mean or changes in the variability of the process. When identifying these shifts, there are the two types of errors that must be avoided: (1) Type I, which are out-of-control signals due to only random variation (false alarms), and (2) Type II, which are in-control readings when an assignable cause is present. Instrumental in controlling these errors is the particular design of the control chart. The use of control charts requires that three design parameters be specified: the sample size, the sampling interval and the control interval width. The parameters determine the chart's detection capability, often expressed in terms of the Average Run Length (ARL). The ARL is the expected number of samples taken until the chart signals an out-of-control condition. However, not