Role of metrology inaccuracy for variance of test results under reproducibility conditions

Abstract

A source of inaccuracy in regression models is supposed to be the statistical nature of a model and metrology inaccuracy related to the measuring explanatory and response variables. A number of approaches to the assessing inaccuracy of regression models are available. However, their use in searching for a solution to engineering problems concerning the assessing multiple regression inaccuracy is restricted by insufficiently developed mathematical tools. When explanatory variables assigned appropriately the inaccuracy of a regression depends on the reproducibility of test results. The reported simulation study investigates the importance of a measurement error to the variance of a normally distributed random variable for small sample sizes between 2 and 30 and coefficients of variation 1, 2, 10, 20, 40, 60. The effect of inaccuracy is analyzed relying on a relative confidence interval of variances estimated as a difference between variance intervals for a variable measured inaccurately and accurately divided by a confidence interval of the variance for an accurately measured variable. The outcomes to emerge from the study are quantity-related estimates for the effect of metrology inaccuracy in the measuring random variables with various coefficients of variation for small sample sizes and different relative measurement errors. For the assessing we use 106 retests and a maximal variance for the same number of repeated tests. The results make possible to evaluate an effect of metrology inaccuracy for diverse coefficients of test results variation, as well as determine an appropriate extent of testing for assigned model inaccuracies and a known measurement error. In addition, practical application of obtained results is shown.