Continuous Sampling Plans

In the sampling of some processes, lots are not clearly defined. In a sense, lot size is N¼ 1, since units are produced item by item. Examples might be cars coming off an assembly line, soft drink bottles from a continuous glass ribbon machine, or welded leads emanating from a welding operation. Yet average outgoing quality limit (AOQL) and perhaps some form of lot tolerance percent defective (LTPD) protection may be desired. Sometimes in such situations, it is possible to artificially define a lot, such as the production of an hour, a shift, a day, or a week. This is often quite arbitrary, however, and other alternatives exist. Emanating from the original CSP-1, published by Dodge (1943), several different continuous

sampling plans have been developed to deal with this situation, usually with AOQL protection. They apply to a steady stream of individual items from the process and require sampling of a specified fraction, f, of the items in order of production, with 100% inspection of the flow at specified times. Several such plans have been described in detail by Stephens (1980) in a manual prepared for the American Society for Quality Control. Special measures of performance apply to continuous plans, they include

AOQ¼ average outgoing quality AOQL¼ average outgoing quality limit Pa¼ average fraction of production accepted under sampling AFI¼ average fraction of production inspected

The AOQ and AOQL are previously defined. The symbol Pa is used to denote the average fraction of production accepted under sampling since in concept Pa implies the probability of an item being accepted on a sampling basis (whether included in the sample or not). In this sense, Pa will be seen to be analogous to the lot-by-lot probability of acceptance under rectification. AFI indicates the average fraction of product actually inspected including items inspected during sampling or in screening. Then

Pa ¼ 1 AFI1 f

The most celebrated continuous sampling plan and the plan which undoubtedly has received the most application is also the original-the Dodge CSP-1 plan. It is carried out on a stream of product, with items inspected in order of production. The procedure is as follows:

1. Specify sampling fraction ( f ) and clearing interval (i).