**5. Conclusion**

*<sup>R</sup>*ð Þ¼ *<sup>τ</sup><sup>c</sup> <sup>P</sup>*ð Þ� *<sup>τ</sup><sup>c</sup> <sup>U</sup>*ð Þ¼ *<sup>τ</sup><sup>c</sup> <sup>P</sup>*<sup>∗</sup> ð Þ� *<sup>τ</sup><sup>c</sup> <sup>U</sup>*ð Þ *<sup>τ</sup><sup>c</sup> :* (20)

*<sup>R</sup>*ð Þ¼ *<sup>τ</sup><sup>s</sup> <sup>P</sup>*<sup>∗</sup> ð Þ� *<sup>τ</sup><sup>s</sup> <sup>U</sup>*ð Þ *<sup>τ</sup><sup>s</sup> ,* (21)

Risk *R*(*τc*) is possible to consider as risks of the implemented unfavorable events

This time can be situated in the interval *τ<sup>c</sup>* ≤ *τ*<sup>1</sup> ≤ *τ*2. Then, for one operated unit of the NPP, the common risk at reaching the given i-group of limiting state from the

7

*i*¼1 *<sup>R</sup>*ð Þ *<sup>τ</sup><sup>c</sup> <sup>i</sup>* (22) .

If at loss estimations to consider not only direct losses at occurrence of unfavorable event *U*(*τ*к) together with complementary losses *U*(*τ*1) and *U*(*τ*2), then it is

*U*ð Þ*τ* . <sup>Σ</sup> ¼ *U*ð Þþ *τ<sup>c</sup> U*ð Þþ *τ*<sup>1</sup> *U*ð Þ *τ*<sup>2</sup> (23)

7

*i*¼1

*U*ð Þ *τ*<sup>Σ</sup> *<sup>i</sup>*

On the basis of results of an estimation considered above risk components, it is possible to build dependences between basic parameters of risk for the NPP probabilities *P*(*τ*) occurrence of unfavorable situations and losses *U*(*τ*) from them

The line had above and design points in the **Figure 21** belong to probabilities *P*(*τc*) and to losses *U*(*τc*) for the moment of accident or disaster occurrence on the NPPs. The lower line made like overhead characterizes a negligible zone of risk parameters *P*ð Þ *τ<sup>c</sup>* ½ �min � *U*ð Þ *τ<sup>c</sup>* ½ �min and the midline characterizes a zone of acceptable risks *P*ð Þ *τ<sup>c</sup>* ½ �� *U*ð Þ *τ<sup>c</sup>* ½ �. If to allow common (near-term and long-time)

*<sup>P</sup>*<sup>∗</sup> ð Þ *<sup>τ</sup><sup>s</sup> <sup>i</sup>*

*:* (24)

*<sup>R</sup>*ð Þ *<sup>τ</sup><sup>c</sup>* <sup>Σ</sup> <sup>¼</sup> <sup>X</sup>

at *τ<sup>i</sup>* = *τ<sup>c</sup>* and to use them for prediction of events for times *τ<sup>i</sup>* ≥ *τc*. One such prospective risk appears as the risk for the current phase of service *τ<sup>i</sup>* = *τs*. In this

case, on the basis of Eq. (19), it is possible to write

possible to define common (integral) losses as

*Parameters of risks for the NPP with reactors of VVER types.*

LS-7 to the LS-1 will constitute

*Probability, Combinatorics and Control*

(**Figure 21**).

**Figure 21.**

**214**

where *τ<sup>s</sup>* is the time after unfavorable event (*τ<sup>s</sup>* ≥ *τc*).

These integral losses respond to the appropriate risks

*<sup>R</sup>*ð Þ *<sup>τ</sup>*<sup>Σ</sup> <sup>Σ</sup> <sup>¼</sup> <sup>X</sup>

From stated above follows that the major problems which have been not decided while to the full for a NPP there are problems of provision of their protectability and safety on the basis of new scientific fundamental and application researches on mechanics, hydrodynamics, economics, mathematical and physical modeling of dangerous processes resulting to heavy disasters, and also development of detailed methods of the analysis of risks for heavy disasters.

Results of the fulfilled scientific researches and developments in this direction, integrated [3–8, 15–17] in the serial of monographic publications on strength, life time, and safety of power nuclear reactors, are initial scientific baseline for the applicable normative, designer, technological solutions on provision of protectability of the NPP equipment from heavy disasters on the basis of criteria of acceptable risks.

The above-mentioned results of analytical and experimental researches can be considered in the capacity of a theoretical basis for the subsequent development of practical models of the computational analysis of risks for strategically relevant installations of a nuclear energetic on the basis of the complex Eqs. (1)–(24). Development of such models, and the most important—their filling up statistically reliable probability distribution of fractures on groups of limiting states (see **Table 3**) on the one hand, and economical computations of losses, with another, it is necessary to consider as the major task for a solution of a problem of safe development of power supply of human community.

At up-to-date and subsequent stages of evolution of power engineering in Russia in the capacity of a basic recommended position, it is necessary to use the position about provision of an acceptable risk level of occurrence of accidents and disasters. In this connection, it is not obviously possible to ensure from social-economic and technological stands the declared principle of absolute safety with null risks (*R* (*τ*) = 0). Owing to it, the solution of the delivered problem is brought together to determination of scientifically well-founded admissibility of occurrence of the emergency situations with possible minimization of loss caused by them, with an estimation of the greatest possible, acceptable, and controlled risk both at probable occurrence of global and national accidents and disasters, and their realization at regional and local levels.
