Sample Survey Method

The method of sample surveys is based on two theories of mathematical statistics - selection from a finite population and selection from an infinite one. The differences are that the first case relates to objects of nonrandom nature, such as defective products or sociological phenomena ^[2] , and the second extends to the results of random processes, for example, measurement errors of some parameters.

Particular attention is paid to the sampling process. It, in accordance with the theory of probability , will correctly reflect the properties of the entire population only if the choice is made by chance . That is, any sample should have the same probability of occurrence.

Note that in practical research, selection without return is usually used (sampling without repetition). In this case, each selected object is extracted from the general population and does not take part in the further process. Selection with return (sampling with repetition) is found, as a rule, only in theoretical studies.

Properties studied by selective methods are divided into qualitative and quantitative. In the first case, the objective of the study is to determine the number of objects with certain characteristics (quality). For example, in social studies this may be the number of individuals who advocate certain views. Then, the evaluation criterion may be the share of such persons in the total population. In the case of a quantitative study, for example, determining the income of different age groups, the average value of income (mathematical expectation) for each group is revealed, and the sample average becomes the evaluation criterion ^[1] .

The variability of the results obtained by selective methods is evaluated by the so-called dispersion of the studied parameter . The accuracy of the results, or their error, is calculated as the square root of the variance and is called the standard deviation .

A type of sample survey, which has become widespread in production, is the statistical control of product quality and technology. As noted, in its frames use the choice from the final totality ^{[1] [3]} . In the Soviet Union in the early 70s of the XX century, one of the founders of such control and quality management based on it, in particular welding , was V. N. Volchenko , professor of the department of welding and diagnostics technology of MSTU named after N. E. Bauman ^[4] .

Statistical control usually involves the use of tools such as the Pareto chart, cause and effect chart, control charts, histograms, stratification method, graphs, and scatter diagrams ^[5] .

In industry, for conducting statistical control, graphical material is most widely used, for example, the so-called Levey-Jennings diagrams . They are a graph where the X-axis records the temporal characteristics, and the Y-axis displays a certain digital parameter, which is an indicator of quality . For example, the level of defectiveness. In addition, the graph contains several contour lines corresponding to the average value of the quality indicator ( mathematical expectation ) and two or three standard deviations from it, and, depending on the tasks, deviations corresponding to the level of sorting. Monitoring the actual position of the investigated digital parameter in the diagram provides a quick visual indication of the current quality level, which allows you to quickly identify its unacceptable deviations and, if necessary, to help eliminate them ^[3] .

• Quality control
• Statistical Process Management
• Shekhart's control card

• Dunin-Barkovsky I.V., Smirnov N.V. Probability theory and mathematical statistics in engineering (General part), Moscow: GITTL, 1955., p. 566.
• Belyaev Yu. K. Probabilistic methods of selective control, M., 1975.