A general model for the optimal economic design of X¯ charts used to control short or long run processes

A new model is presented for the optimal design of X¯ charts utilized for the statistical monitoring of processes where production runs have a finite duration. The proposed model considers the effect of the setup operation on the chart design. The model contains both Duncan's model and a model due to Ladany as particular cases, yet it allows the user to consider more realistic production environments. Two types of finite-length production process are considered: a repetitive manufacturing process and a job-shop process. New relationships between the length of the production run, the power of the chart and the nature of the process setup are found by numerically analyzing the behavior of the model.