THE ECONOMIC DESIGN OF CONTROL CHARTS: A RENEWAL THEORY APPROACH

Abstract

Economic models for the design of control charts based on Duncan's approach1 have been well studied in the recent past. We present an alternative approach to the development of a few of these models using renewal equations. The main emphasis here is to study the role of the probability model associated with the process failure mechanism. It is demonstrated that the expressions Tor the expected cycle length E( T) and the expected cost per cycle E( C) are easier to obtain by the proposed renewal equation approach than by adopting the traditional approach. Furthermore, it is observed that certain non-Markovian shock models may be analyzed by adopting a renewal equation approach, whereas Duncan's approach has not been used with any non-Markovian model.