Some Recent Developments in Control Charts for Monitoring a Proportion

Abstract

Marion R. Reynolds, Jr. Virginia Polytechnic Institute and State University, Blacksburg, Virginia Zachary G. Stoumbos Rutgers University, Newark, New Jersey 1. INTRODUCTION Control charts are used to monitor a production process to detect changes that may occur in the process. In many applications, information about the process may be in the form of a classification of items from the process into one of two categories, such as defective or nondefective, or nonconforming and conforming. The process characteristic of interest is the proportion p of items that fall in the first category. For convenience in describing the problem being considered, the labels “defective” and “nondefective” will be used in this paper for the two categories. It is usually assumed that the items from the process are independent with probability p of being defective. This would then imply that the total number of defective items in a sample of n items, say 7\ has a binomial distribution. In most quality control applications the primary objective in using a control chart would be to detect an increase in p , because an increase in p corresponds to a decrease in quality. However, a decrease in p would be of interest if it is important to document an improvement in process quality. Woodall (1997) gives a gen­ eral review of control charts that can be applied to the problem of monitor­ ing p.

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