Estimating quantiles in acceptance criteria for structural components

Abstract

The probabilistic foundations of methods to control the characteristic properties of structural materials, expressed as p-quantiles, are discussed. We argue that the acceptance criteria in the quality control should be based on quantile estimators complying with the definition of the quantile. We introduce the distribution-free concept of definition-based quantile estimator. For normal distribution, an application of different types of estimators, as well as some attribute methods and mixed methods presently used, are illustrated by operating characteristic curves. We recommend the prediction method by which the subjective limit values of the mixed methods are eliminated, information from the sample will be used more effectively than in the attribute methods, and the questions about the proper confidence level or a “known” variation coefficient need not be considered. However, the direct application of the prediction method results in stricter quality control than that presently used. Therefore, we recommend adopting p’ > p in such a way that if the predicted p’-quantile estimate  is equal to or higher than the lower lilmit L, the required value of the p-quantile, the lot is accepted in the quality control. If the present quality level is appropriate, the value of p’ can be chosen in such a way that the present level is maintained. If not, necessary modifications are possible simply by adjusting p’.