Computer information technology for processing measurements in monitoring and control tasks

Abstract

Measurement is the main source of information about the condition and quality of developed and modernized technical objects and technological processes. The measured indicators characterizing them are random variables. In the tasks of observation and control of technical objects, measurement samples are compared, and decisions are made on them about their condition. Difficulties in solving such problems occur if the measurement samples are short and their statistical laws are unknown. They contain information about the state of objects, about their stability or change.
Samples of experimental measurements contain information about the state of automated systems. By evaluating and comparing their average values, sample variances, histograms, the tasks of observing their state are solved. Difficulties occur if the samples are short and statistical patterns are unknown.
Classical mathematical statistics offers for their solution the two-sample Anderson criterion - the empirical expectation of the difference of two continuous probability distribution functions formed from ordered samples of experimental measurements. A solution to these problems is proposed by forming discrete probability distribution functions of experimental measurement samples and estimating the mean square of their difference. This is an analogue of the Anderson criterion.
To test hypotheses about the statistical laws of experimental measurements, their continuous functions of probability distribution, instead of the Smirnov-Kramora-von Mises criterion, apply a more consistent discrete criterion - the average value of the square of the difference of the theoretical probability distribution function and the discrete function generated from the experimental measurements.
By means of computational experiments, the statistical laws of discrete criteria for comparing short experimental measurement samples with symmetric (normal, logistic) and asymmetric (Rayleigh) probability distribution laws have been investigated. The histograms of discrete criteria for assessing their statistical homogeneity are analyzed. The statistical laws of the discrete criteria do not differ from the statistical laws of the Anderson criterion and the Smirnov-Cramer-von Mises criterion, but practical application in the tasks of testing hypotheses is much simpler than their analogues.