Sampling inspection permits the estimation of the overall quality of a group of product articles through the inspection of a relatively small number of product articles drawn from the group.
The specification of a sampling plan provides purchasers and sellers a means of identifying the minimum quality level that is considered to be satisfactory.
Because sampling plans yield estimates of the quality of a product, the results of the inspection are subject to error. Through the selection of a sampling plan, the potential error is known and controlled.
Sampling inspection is used when a decision must be made about what to do with a quantity of articles. This quantity may be a shipment from a supplier, articles that are ready for a subsequent manufacturing operation, or articles ready for shipment to a customer.
In sampling inspection, a relatively small number of articles (the sample) is selected randomly from a larger number of articles (the inspection lot); the sample is inspected for conformance to the requirements placed on the articles. Based on the results, a decision is made whether or not the lot conforms to the requirements.
Since only a portion of a production lot is inspected, the quality of the uninspected articles is not known. The possibility exists that some of the uninspected articles are nonconforming. Therefore, basic to any sampling inspection plan is the willingness of the buyer to accept lots that contain some nonconforming articles. The number of nonconforming articles in accepted lots is controlled by the size of the sample and the criteria of acceptance that are placed on the sample.
Acceptance sampling plans are used for the following reasons:
When the cost of inspection is high and the consequences of accepting a nonconforming article are not serious.
When 100 % inspection is fatiguing and boring and, therefore, likely to result in errors.
When inspection requires a destructive test, sampling inspection must be used.
In acceptance sampling by variables, the coating characteristic of each article in the sample is measured. Using the arithmetic mean of these values, the standard deviation of the process, and the factor k that is found in the Tables, a number is calculated (see 9.3). If this number equals or exceeds the specified minimum, the inspection lot conforms to the requirements. If it is less, the lot does not conform. If the standard deviation of the process is not known, the standard deviation of the sample is calculated and used.
The use of a sampling plan involves the balancing of the costs of inspection against the consequences of accepting an undesirable number of nonconforming articles. There is always a risk that a random sample will not describe correctly the characteristics of the lot from which it is drawn, and that an unacceptable lot will be accepted or an acceptable lot will be rejected. The larger the sample, the smaller this risk but the larger the cost of inspection.
To understand the risks, consider that if every article in an inspection lot conforms to its requirements, every article in the sample will conform also. Such lots will be accepted (Note 1). If only a few articles in an inspection lot are nonconforming, the sample probably will indicate that the lot is acceptable; but there is a small probability that the sample will indicate that the lot is unacceptable. The larger the proportion of nonconforming articles in an inspection lot, the more likely it will be that the sample will indicate that the lot is unacceptable. If every article in an inspection lot is nonconforming, a sample will always indicate that the lot is unacceptable.
Note 18212;Throughout this method, it is assumed that no mistakes are made in sampling, measurement, and calculation.
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