An optimal set-up policy for control charts

A model of a production process, using an unscheduled set-up policy and utilizing fraction-defective control charts to control current production is developed taking into consideration all the costs; namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of re-adjusting detected changes. The model is based on the concept of the expected time between detection of changes calling for set-ups. It is shown that the combination of unscheduled set-ups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval and extent of control limits from process average will be used that provide the minimum expected total cost per unit of time. The costs when a production process with unscheduled set-up is controlled by using the appropriate optimal control charts is compared to the cost of a production process using scheduled set-ups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled set-ups using optimal set-up intervals over unscheduled set-ups. Suggestions are made to evaluate the optimal process set-up strategy and the accompanying decision parameters, for any specific cost data, by use of computer enumeration.