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Control charts based on grouped observations

It is often more economical to classify a continuous quality characteristic into several groups than it is to measure it exactly. We propose a control chart based on gauging theoretically continuous observations into multiple groups. This chart is designed to detect one-directional shifts in the mean of a normal distribution with specified operating characteristics. We show how to minimize the sample size required by optimizing the criteria used to group the quality characteristic. Control charts based on grouped observations may be superior to standard control charts based on variables when the quality characteristic is difficult or expensive to measure precisely but economical to gauge.