Abstract In continuous production processes, where items are produced sequentially, the application of a continuous sampling inspection technique for the purpose of controlling or maintaining quality is sometimes more effective than the application of other types of techniques, such as lot-by-lot sampling inspection. In this article, a multilevel continuous sampling procedure is devised. Its long-run statistical properties, the AOQ function and AFI function, are derived by demonstrating the operation of the procedure as a finite Markov chain. This procedure is presented with the change in sampling rates in both geometric and arithmetic progression. Two initial sampling rates are given as 1/2 and 1/3. The flow process chart, some tables of AOQ and AFI functions, and the tables of the relevant parameters which yield a specified AOQL are presented to facilitate the application of these plans.
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