Multivariate Sampling Plans in Quality Control: A Numerical Example

This paper presents an attributes acceptance sampling procedure where several measurements are available on each item in the sample set. It is thus especially relevant when these measurements on each item are correlated; usual procedures cannot account for correlations. Correlations are considered by using a classification rule to assign the attribute good or bad to each item in the sample set; this rule uses the non-parametric k-nearest neighbor estimator. The test by which the lot is accepted or rejected, based on the outcomes of the rule for all items in the sample set, is the same as in acceptance sampling by attributes. The estimator has only to be compensated for errors at the level of the classification rule. This procedure has been used since 1978 in industry, thanks to a software package which implements it. Applications have mostly been to process quality control and mechanical parts. The procedure has the interesting feature of applying under relaxed assumptions on the distributions of the measurements on the bad items. The numerical example covers such a case. Because the classification rule operates individually on each sample item, nothing is changed in the definitions of the acceptable quality level and the limiting quality level. They apply to the whole lot. This is true because the multivariate measurements on each item are aggregated into a binary attribute on each item, as in classical sampling by attributes.