Визначення оптимального об`єму вибірки при проведенні експериментальних досліджень

Abstract

В роботі розглянуто варіанти оцінок вибірок довільного обсягу. Для них вирішується питання визначення мінімального обсягу вибірки, щоб отримана оцінка параметра розподілу або початкових умов задовольняла встановлені вимоги до проведення вимірювань з необхідною точністю

The variants of estimations of selections of arbitrary volume are considered in work. The question of determination of minimum sample size decides for them, that the got estimation of parameter of distributing or initial conditions satisfied the set requirements to conducting of measurings with necessary exactness. The use of a particular technique depends on the a priori information about the parameters of the distribution of random errors. If such information is not available, extensive experimental studies should be carried out. The article analyzed the ways of determining the optimal volume of tests in conducting multiple measurements of physical quantities and obtained analytical expressions for various cases concerning a priori information about the parameters of the distribution of random errors of measurement results. The use of the function of most plausibility is appropriate for a sufficiently large sample size. With a known confidence rating, with a measure of reliability, the sample size is determined with the help of t-distribution of the Student. To determine the membership of a sample to the general population, the required number of multiple measurements is determined at a known boundary, which estimates the errors of the 1st and 2nd kind. The ratios given in this article make it possible to reduce the cost of conducting research, which in many cases requires significant financial costs