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The work is devoted to the analysis of non-standard methods for assessing reliability and the probability of uptime (operating time) to failure at a certain point in time. In the case of small deviations in the density of the failure distribution from the normal type, the perturbation function method is considered, which is applicable to a wide class of distributions decreasing at infinity no faster than the exponential function. For processing censored runs, when only the number of runs for certain periods of observation time is known, estimates of the distribution function from start to failure and the probability of uptime are obtained based on the application of the root method of nonparametric construction of the distribution density of a random variable. In contrast to strictly probabilistic methods of reliability analysis, diffusion distributions as probabilistic-physical models of reliability have a great practical advantage. The method of constructing the failure distribution function proposed in the article provides a reasonable choice of a theoretical distribution model from a fairly complete set of competing distribution models, which must necessarily include monotonic and non-monotonic diffusion distribution. The results of the study of reliability estimates and the probability of trouble-free operation in relation to dangerous failures allow to assess the level of safety of complex technical systems containing hazardous production facilities. An analytical expression has been obtained for the probability of trouble-free operation of a system with automatic protective devices that ensure the safety of maintenance personnel at hazardous production facilities
Bagir-zadeh et al. (Tue,) studied this question.