3. Some basic probabilistic models for risk prediction

instead of input data for modeling. Estimate, please: if to be guided by these frequencies and to consider that 50–70% of failures are the result of "human factor," it should mean that the frequency of critical errors from "human factor" on systems is about one time in thousand years! However, that is not so in real life! Errors are committed much more often. But they are under control, and the majority of them is in due time corrected. As consequence of these counteraction measures, required system integrity (including safety) is reached. The answer arises obviously: the frequency λ of system integrity losses used at risk predictions itself should pay off by the results of probabilistic modeling. Indeed, for adequate risk prediction, there is an important frequency of all the primary incidents (including neutralized incidents at the expense of control

Consideration of "smart" system possibilities for proactive diagnostics of system integrity, monitoring of conditions, and recovering the lost integrity allows to create more adequate

Figure 4. The possible variants of correlations of the limitations to admissible risks, exponential, and an adequate PDF of

Figure 5. All requirements to admissible risk are met for an adequate PDF of time between losses of system integrity.

time between losses of system integrity with identical frequency of system integrity losses λ.

measures, maintenance, and timely reaction on initial signs of threat development).

28 Probabilistic Modeling in System Engineering

Considering possibilities of "smart" systems, two general technologies of providing protection in different spheres are described: proactive periodical diagnostics of system integrity (technology 1) and additionally monitoring between diagnostics (technology 2) including recovery of integrity [2–3, 6–10]. These models allow to create more adequate PDF of time before the next event of the lost integrity.
