Minimum Average Total Inspection Plans for Variables Sampling, Indexed by Average Outgoing Quality Limit

Abstract

Dodge and Romig's 1944 volume Sampling Inspection Tables provided, among other procedures, sampling inspection plans for attributes inspection which were indexed by average outgoing quality limit. These tabulated plans guaranteed that when rejected lots are appropriately treated, the long-term average outgoing product quality would not exceed the average outgoing quality limit (AOQL) index of the plan. In addition, the plans were structured so that when the submitted quality level was at the indicated level of process average, the total amount of inspection would be minimized. In this article, plans are presented that match the AOQL, lot size, and process average parameters of the Dodge and Romig plans, but are based on variables sampling rather than attributes sampling. It is assumed that the distribution of the measured characteristic is Normal. Although measurements data are usually more difficult to obtain than attributes data and more calculation is involved in using the plans, the sample sizes are generally substantially smaller. The exception to this is for unknown standard deviation plans, higher AOQL index, and process average near the listed AOQL. It would be presumed that in present-day applications, plans involving low levels of both process average and AOQL would be most widely used.