New Rule to Incorporate Inspection Errors in Process Control Using Markov Chains

A number of authors have considered the procedure of online process control in which every hth item produced is inspected. The process is judged to be in control and continues if the inspected item is judged to conform to specifications. If the inspected item is judged to be nonconforming, then the process is judged to be out of control and stopped, examined, and adjusted as necessary. This inspection process is subject to misclassification and different schemes have been suggested for dealing with this. In this paper, we propose a new rule in which the final judgment that an item is conforming, and thus the process is in control, if and only if k consecutive classifications as conforming occur before a total of f classifications as nonconforming. We will examine various aspects of this protocol and provide advice on how to determine values of k and f for this rule.