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Improved Curtailed Sampling Plans for np Control Charts

Summary: The use of fully curtailed sampling in monitoring the proportion of nonconforming items is considered. In the usual np control chart with an upper control limit, complete sampling is used; that is, every item in a sample of size n is inspected and the process is declared to be out of control if m or more nonconforming items are found. Under full curtailment, it may not be necessary to sample and inspect all n items; sampling and inspection are halted if either m nonconforming or n - m + 1 conforming items are found. In the former case, the process is declared to be out of control; in the latter it is declared to be in control. In this article, economic criteria are used to select the values of n, m, and k (the inter-sample interval) that minimize the total expected cost of a given control procedure. Fully curtailed sampling is compared to both semi-curtailed (in which out-of-control is declared as soon as m nonconforming items are found) and complete sampling for over 175 combinations of cost coefficients and process parameters. The results indicate that full curtailment can yield substantial improvement in expected cost over both of the other sampling policies, especially when one considers the expected savings in absolute cost over an extended period of time.

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  • Topics: Sampling
  • Keywords: Sample size,Sampling plans,Nonconformities,Economic design,Cost analysis,Control limits
  • Author: Williams, William W.; Looney, Stephen W.; Peters, Michael H.
  • Journal: Journal of Quality Technology