Sampling Plans
A “lot,” or batch, of items can be inspected in several ways, including the use of single, double, or sequential sampling.
Single Sampling
Two numbers specify a single sampling plan: They are the number of items to be sampled (n) and a prespecified acceptable number of defects (c). If there are fewer or equal defects in the lot than the acceptance number, c, then the whole batch will be accepted. If there are more than c defects, the whole lot will be rejected or subjected to 100% screening.
Double Sampling
Often a lot of items is so good or 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 n1 sample is between c1 and c 2 , 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.
Sequential 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 calledsequential 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.
Selection of the best sampling approach—single, double, or sequential—depends on the types of products being inspected and their expected quality level. A very low-quality batch of goods, for example, can be identified quickly and more cheaply with sequential sampling. This means that the inspection, which may be costly and/or destructive, can end sooner. On the other hand, in many cases a single sampling plan is easier and simpler for workers to conduct even though the number sampled may be greater than under other plans.
