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Sampling plans performance

When a customer recieves a lot (could be final products for resale, raw materials to be processed, intermediate product to be inspected ... etc), he performs inspection to make sure the lot satisfies the level of quality needed. Inspection is usually done by randomly selecting one sample (single sampling) or several consequtive samples (multi-sampling). Samples are inspected (checking of product dimensions, lifetime, bearable load, chemical composition ... etc) and the whole lot will be accepted if the number of defects found in the sample doesn't exceed a certain number called acceptance number.

The procedure above is called a sampling plan. A sampling plan is said to be good if it causes good lots to be accepted, and bad ones to be rejected. The performance of any given sampling plan mainly depends on the number of products per sample, and on the value of the acceptance number.

Performance of a plan can be judged using Operating Characteristic curves (O.C. curves). This is a graph of the lot quality (total percentage defective) on the X-axis and the probability of accepting the lot on the Y-aixs. For example, if the contract between a supplier and a consumer implies that lot percentage defective must not be greater than 3%, and the actual lot delivered has a percentage defectives higher than 3%, an ideal sampling plan would reject the lot at 100% of the cases. But if the lot has less than 3% defective products, the ideal plan would accept the lot at 100% of the cases.

However, actual sampling plans do not behave so ideally. A good sampling plan would accept a lot of 4% defectives in only 2 or 3% of the cases. A bad one would accept it at 10% or more of the cases. The O.C. curve helps us to judge the performance of any given plan.

Our program plots the OC curve given the number of samples and the acceptance number. To download the C source code, click here. To download a PC-compatible DOS executable version, click here.

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