Often a lot of items may be so good or may be so bad that we can reach a conclusion about its quality by taking a smaller sample than would have been used in a single sampling plan. If the number of defects in this smaller sample (of size n1) is less than or equal to some lower limit (c1), the lot can be accepted. If the number of defects exceeds an upper limit (c2), the whole lot can be rejected. But if the number of defects in the n1sample is between c1 and c2, a second sample (of size n2) is drawn. The cumulative results determine whether to accept or reject the lot. The concept is called double sampling.
Multiple sampling is an extension of double sampling, with smaller samples used sequentially until a clear decision can be made. When units are randomly selected from a lot and tested one by one, with the cumulative number of inspected pieces and defects recorded, the process is called sequential sampling. If the cumulative number of defects exceeds an upper limit specified for that sample, the whole lot will be rejected. Or if the cumulative number of rejects is less than or equal to the lower limit, the lot will be accepted. But if the number of defects falls within these two boundaries, we continue to sample units from the lot. It is possible in some sequential plans for the whole lot to be tested, unit by unit, before a conclusion is reached.
