This article introduces an approximation that is useful for plotting the operating characteristic curves of sampling plans in which the sample is assumed to be randomly drawn from a normal distribution and the acceptance criteria involve limits for the sample mean and for individual sample observations. An exact computing procedure is developed, and numerical results are presented to verify the accuracy of the approximation for small samples.

Brown and Fisher (1972) proposed a model for subsampling mixtures of sampled material and used it to analyze an elementary composite sampling procedure. Their results and the results of Rohde (1976) are extended to cover procedures with several finite composites, testing error and within-increment variability. Among the properties of composite sampling procedures derived are the following: (1) the composite sampling estimator of a lot mean (μ x ) is unbiased whether or not the subsampling procedure in unbiased, (2) there is a relative upper bound on the variance of the composite sampling estimator of μ x , and (3) it is not necessary to form more than one composite to check for changes in basic parameters from lot to lot. The impact of these and other properties on the process of choosing a composite sampling procedure is discussed. KEY WORDS: Bilinear formsBulk samplingComposite samplingVariance components

This paper presents a procedure for matching double sampling plans to given single sampling plans. The procedure assumes sampling from a normal distribution with known standard deviation and assumes that lot average is the property of interest. It is applicable, for example, to sampling of bulk material. Double sampling plans with the “best” average sample size are discussed. An example shows how to use the procedure to find approximately matching double and single sampling plans for sampling from a binomial distribution. KEY WORDS: Double SamplingNormal DistributionAverage Sample SizeLot AverageBinomial Distribution