heizer10e_tut2 - Online Tutorial Acceptance Sampling 2...

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Online Tutorial 2 Acceptance Sampling Tutorial Outline SAMPLING PLANS Single Sampling Double Sampling Sequential Sampling OPERATING CHARACTERISTIC (OC) CURVES PRODUCER’S AND CONSUMER’S RISK AVERAGE OUTGOING QUALITY S UMMARY K EY T ERMS S OLVED P ROBLEM D ISCUSSION Q UESTIONS P ROBLEMS
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T2-2 CD T UTORIAL 2 A CCEPTANCE S AMPLING In the Supplement to Chapter 6, “Statistical Process Control,” we briefly introduced the topic of acceptance sampling. Acceptance sampling is a form of testing that involves taking random sam- ples of “lots,” or batches, of finished products and measuring them against predetermined standards. In this tutorial, we extend our introduction to acceptance sampling by discussing sampling plans, how to build an operating characteristic (OC) curve, and average outgoing quality. 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 n 1 ) is less than or equal to some lower limit ( c 1 ), the lot can be accepted. If the number of defects exceeds an upper limit ( c 2 ), the whole lot can be rejected. But if the number of defects in the n 1 sample is between c 1 and c 2 , a second sample (of size n 2 ) is drawn. The cumula- tive 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 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. 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
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