The article describes the approach to industrial safety (reliability) assessing with limited statistical information by quantity and quality at the same time. The quantitative data incompleteness is modeled by the distribution functions based on Chebyshev’s inequality which can be used only if the estimates of mathematical expectation and standard deviation are known. Qualitative incompleteness of statistical data is modeled by belief and plausibility functions based on the evidence theory. Qualitative incompleteness of statistical data refers to the representation of individual values of a random variable in the form of intervals. The proposed approach allows obtaining a safety (reliability) assessment based on available information without assumptions and hypotheses about the distribution functions of random variables and the estimation of the individual parameters of distribution functions. Verification of the proposed approach is demonstrated by the numerical example where the initial data is obtained by pseudo-random numbers simulation (Monte Carlo simulation). The results of the numerical example show that the reliability interval obtained by proposed approach for limited statistical data covers the theoretical reliability value for full statistical data. Extended belief and plausibility functions based on the robust Dirichlet model help to obtain a more cautious estimate by introducing a data «uncertainty» factor. The proposed approach to reliability analysis can be used to assess the safety of any industrial facilities and processes by reducing a limit state mathematical model the classical form X ≤ Y.

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