Abstract
Abstract : The optimal statistical control of a simple production process which has only two underlying states, good and bad, is studied. The produced items are classified as good or defective, a cost being associated with each defective item produced. A cost is also charged for repairing the process, which has the effect of returning the process to the good state. Other than immediately after repair, the process state is assumed unknown. One seeks a statistical control rule which, based on the quality history of produced items, tells when to repair the machine. A feasible means of computing the control rule which minimizes the average cost per unit time is given. The nature of the solution is such that once tables of operating characteristics have been prepared, the solutions to a wide variety of problems may be had through slight additional hand calculations. The optimal rule is shown to be relatively insensitive to errors in estimating the model parameters. A means of checking, over a long period of time, whether or not estimates are correct has also been suggested.
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