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Estimating a Proportion from Repeated Sampling of a Growing Population

Summary: The authors consider estimating the proportion of a growing population having a specified manufacturing anomaly from data obtained by repeatedly sampling the population as it grows. The observed proportion, though easily calculated, is biased. The Horvitz-Thompson (HT) estimator, commonly used in survey sampling, accounts for the unequal probabilities with which units are selected in this sampling design to produce an unbiased estimator of the population proportion having the anomaly. We derive the form of the HT estimator and an unbiased estimator of its variance that can be used to assess the uncertainty of an HT estimate. The authors consider an illustrative example to show the benefit of using survey sampling theory and present how simulation might be used to estimate the inclusion probabilities.

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  • Topics: Sampling
  • Keywords: Bias, Ratio estimates, Population variance, Defense industry, Random sampling, Manufacturing
  • Author: Hamada, Michael S.; Lohr, Sharon L.; Hamada, Christina A.; Burr, Tom
  • Journal: Quality Engineering