The effect of nonnormality on variables sampling plans

Acceptance sampling plans based on variables have been in use for many years. Recently, there has been a renewal of interest in these plans, because of the relative efficiencies that they offer with respect to attributes sampling regarding sample size. Furthermore, in situations where acceptable quality levels are very small, and a high level of protection is desired, variables sampling is often much more efficient than attributes sampling. An important disadvantage of variables sampling is that the distribution of the parameter being inspected must be known. Most standard variables sampling plans assume that the distribution of this parameter is normal. This article examines the effect of the normality assumption in variables sampling. Methods to detect departures from normality are reviewed.     

Aggregating assignment constraints

This article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment-type constraints along with other constraints. Several unresolved questions of a number-theoretic nature are mentioned at the conclusion of the article.