Design of attribute control charts for multistage production systems-based on cost criteria

Abstract

This paper develops a method to design attribute control charts, p -charts and c -charts, for multistage production systems based on quality cost criteria. The production systems are structured and formulated as a dynamic programming model. Each productions station and its inspection station is viewed as a combined station and is treated as the stage in the dynamic programming model. The model has quality distribution as the state variable and the stage transformation of this model is also developed. the stage return of this dynamic programming model is the quality cost of implementing an attribute control chart to that stage and the decision variables are the control chart parameters, n -sample size and control limits. Methods to combine quality distributions for finding type I and type II errors are then developed. As the dynamic programming model has quality distribution as state variable, conventional methods of solving dynamic programming problems are not applicable. A method, for solving this model, is thus developed based on branch and bound approach. The method itself may be applied to other dynamic programming problems where conventional methods are inefficient or not applicable. An example of the foundry process of cylinder liners is included to illustrate the developed method.