Determining the value limits of type I and II errors in the decision on the functional suitability or not suitability of the decision support system

DOI №______

Abstract

The environment is changing rapidly in which human conducts its activity. New tasks arise, and as a consequence, appear new decision support systems (DSS). In order to resolve the issue of a suitable or unsuitable DSS for solving tasks, it is necessary to simulate the environment of the DSS activity and to conduct a series of experiments to determine the success or failure of decision-making process.
If the functional probability of making correct decisions to compare with the admissible probability, one can come to the conclusion whether a suitable system or not. But due to the probable nature of the process, it is possible to make a false conclusion, and therefore to decide that the system is not suitable at a time when the system is suitable and vice versa to decide that the system is suitable at a time when it is unsuitable. These errors are called type I and II errors.
In order to decide on the suitability of the system it is not enough to compare the functional probability with the admissible probability, but also need to calculate type I and II errors and compare them with the admissible values. Type I and II errors are calculated using the binomial distribution formula or the Stirling's formula or Poisson's formula.
What values of type I and II errors are admissible?
The article reflects the research of speed and acceleration of changes in the values of type I and II errors and determination of their limits.
The comparative graphs are worked out.
From the graph it is clear that when the admissible probability is equal to the functional probability and with increasing sample size, type I error approaches 0.5.
The conclusions are drawn: when the functional probability is less than the admissible probability it makes sense to take into account only the type I error, as it is argued that the system works properly there is no reason. Accordingly, when the functional probability is greater than the admissible probability it makes sense to take into account only the type IІ error; when the functional probability is less than the admissible probability has meaning only the type I error which is smaller than the values of the type I error, calculated for the functional probability is equals the admissible probability. Accordingly, when the functional probability is greater than the admissible probability has meaning only the type II error which is smaller than the values of the type II error, calculated for the functional probability is equals the admissible probability.
From the graph, it can be seen that the maximum values of the acceleration of the change in value of the type I error fall on 0,26.
The maximum values of the acceleration of acceleration change in value of the type I error fall on 0,034.
The article concludes that the effect of the type I error begins when the functional probability equals 0.72 where the error is 0.034.
The average value of the type I error in 0,26 reaches at the functional probability at 0,77. For DSS of higher quality, admissible errors can be determined in the region of 0.034, for DSS of average quality in the region of 0.26.

Keywords: decision support system; type I and II errors; binomial distribution formula.

References
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