Rectifying Inspection of a Continuous Output

Abstract

The problem discussed is how to choose a plan of rectifying inspection for a continuous output, i.e. for a flow of produced articles not aggregated into lots. It is suggested that the choice of plan should be based on an analysis of the total cost of the operation, and should not depend on arbitrarily assigning an AOQL or other quality guarantee not directly related to the total cost. Three types of inspection plan are considered, namely, no inspection at all, 100% inspection, and sampling inspection according to the type of plan proposed in 1943 by H. F. Dodge. Under certain assumptions, it is shown that an appropriate near-optimum plan can easily be found. Two quantities, denoted by k and M , need to be assessed; the first is a cost factor, the second measures the expected rareness of abrupt deteriorations in the quality of output. When these are specified, the appropriate plan is chosen according to very simple rules explained and summarized in §8. It is suggested that, strictly for the purpose of rectifying inspection (and not for any other purpose, such as process control), Dodge's type of sampling inspection plan can hardly be improved on, unless conditions permit of “deferred sentencing,” the output being held in bond for a while it has passed the inspection point. The principal mathematical difficulty has been to determine the response of a Dodge plan to an abrupt change in quality of output. This is studied in the Appendix. * Paper prepared in connection with research supported by the Office of Naval Research.