Statistical Control of a Gaussian Process

Abstract

The optimal statistical control of a simple production process which has only two underlying states, in control and out of control, is studied. The produced items are assumed to have a measurable quality characteristic which has a normal distribution with known variance. When the process leaves control the mean of thii distribution shifts from μ0 to μ1, both assumed known. Costs are associated with the quality of an item and with repairing the process which returns it to a state of control. Other than immediately after repair, the process state is assumed unknown. This report gives a statistical control rule which, based on the quality history of produced items, tells when to repair the machine. The rule given minimizes the time average of the total cost of repairs plus quality.