Using the Characteristics of the Sample Range of Repeated Observations of a Measurand to Estimate Its Numerical Value and Type A Standard Uncertainty

Abstract

The article lists situations where it is impractical or impossible to record all observation results during repeated measurements, only their minimum and maximum values. The Monte Carlo method is used to analyze the efficiency of various estimators of the expected value for different distribution laws of observation results. The possibility of determining the estimate of the numerical value and type A standard uncertainty of the measurand using the sample range of results of multiple observations is considered, taking into account their number and the distribution law. The Monte Carlo method is used to obtain the dependence of the coefficient for converting the sample range of multiple measurement results into the sample standard deviation for different distribution laws. The novelty of the article lies in the experimental procedure presented for obtaining the dependence of the conversion coefficient on the number of indicating measuring instrument readings without determining their distribution law. An example is provided for evaluating the numerical value and type A measurement standard uncertainty using the parameters of the sample range of measured humidity values from a standard hygrometer. The novelty of this work is the empirical determination of α for real indication measuring instrument (IMI) readings, which can be used to propose calibration-like procedures for range-based assessment.