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Sampling From Batches

Summary: The outputs of many manufacturing processes consist of batches which tend to be more homogeneous than the outputs from the process as a whole. Thus the quality of just one batch is not necessarily representative of the long term quality of the process. This paper discusses a two stage plan for obtaining representative samples of the outputs of such manufacturing processes. The two stage plan is both more efficient and more convenient than simple random sampling. The plan entails sampling k of the batches and subsampling m units within each of the sampled batches. Formulas are presented which determine how k and m should be chosen to maximize the sampling precision subject to cost constraints. Several numerical examples illustrate the adverse effect on precision due to sampling from too few batches. In particular it is shown that drawing the entire sample from just one batch leads to very poor precision.

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  • Topics: Sampling, Statistics
  • Keywords: Sampling plans,Statistics,Optimization,Cluster analysis,Stratification
  • Author: Feder, Paul I.
  • Journal: Journal of Quality Technology