The statistical sampling procedure purports to answer questions such as: (1) are the supplier’s goods to be accepted or rejected? (2) if accepted, what kind of risk do we incur in terms of bad quality? (3) Should the batch, which has been manufactured in our plant, be shipped outside to the customers or not? We are speaking about mass scale procurement of raw materials and of mass scale shipment of finished goods, and hence the use of statistical sampling procedure in answering the accept/reject question.
Why it is not possible to check all items, instead of sampling? The answers are simple (1) Cost of 100% inspection is prohibitive in most cases.(2) Many of the acceptance tests require destructive testing of the item, and therefore a sampling procedure is a must in such cases. (3) Also, 100% inspection does not necessarily ensure 100% quality. Inspection cannot be on to ensure that all accepted products are of good quality. The ‘inspection fatigue’ with repeated inspection operations will very often limit the effectiveness of the inspection. In fact, total inspection (100% inspection) may lead, many a time to less quality than if partial inspection were resorted to (4) Acceptance sampling procedure either accepts or rejects the incoming lot in total. Such an outright rejection of the lot by the consumer often results in remarkable quality improvement on the supplier side. This is an important motivational factor operating in acceptance sampling. (5) Less than 100% sampling makes the inspector carrying out the sampling inspection more responsible towards his job, because a mistake in calling an item good or bad may decide the acceptance or rejection of an entire consignment rather than that of only one item. This greater responsibility forces inspectors to do a better job of inspection. Of course, the earlier mentioned factor of less inspection-fatigue in a sampling procedure also in improving the quality of the inspection procedure itself. These are some of the advantages of the sampling procedure.
One must, however, add that in certain types of products 100% inspection is unavoidable. For instance, Nuclear Power Plant equipment and accessories to the smallest valve or conduit need to be inspected for quality on a 100% basis. We cannot afford to take a sample and based on that accept a consignment because however tight a sampling procedure there is still a chance that few defective items might enter into the nuclear power plant. Only a 100% inspection, with due considerations to the fatigue problem can ensure the requirements of a nuclear power plant. We can also quote instances from the pharmaceutical industry, where in many cases 100% inspection of the drug items becomes essential.
Acceptance Sampling Plan:
Such a clear cut acceptance or rejection of the lot (i.e. probability of acceptance of 1.00 or 0) is not possible when we resort to a sampling procedure. The sampling procedure consists of taking a small sample comprising n number of items from a consignment of N number of items and accepting the consignment only if the number of defective items in the sample is less than or equal to a cut-off number c or else rejecting the consignment. The acceptance sampling plan is therefore expressed as: (N, n, c). The number c is called in technical language as the ‘acceptance number’. In using the acceptance sampling plan, there is a finite probability that the lot may be accepted even of the quality is not really good; also conversely the lot may be rejected even if the quality is actually good. The first type of risk is called the “consumer’s risk” and the second type of risk is called is called the ‘producer’s risk’. In the operating characteristics curve (hereafter abbreviated as OC curve) for 100% sampling, these risks are each zero whereas for any other sampling procedure there exists finite quantities of both risks.
In judging a particular acceptance sampling plan, it will also be necessary to know its performance over a length of time for various possible actual quality levels in the incoming consignment of materials. The OC curve provides us with a complete picture of the various probabilities of acceptance vis-à-vis the possible quality levels of the incoming materials. For any given fraction defective in a lot, the OC curve indicates what percentage of the submitted lots will be accepted ‘in the long run of time’ if a large number of lots of particular quality were submitted for quality inspection.