Author details

The currently developed combined probability statistical method [4] makes it possible to assess the reliability Poð Þ<sup>τ</sup> as a function of time <sup>τ</sup><sup>s</sup> on the basis of analysis of the initial deterministic, statistical, and probabilistic information about the design Кð Þτ and technological Тð Þτ features of MPS objects, the operating loads Qð Þτ and environmental impacts Фð Þτ , stressstrain states in the coordinates σ τð Þ� еð Þτ and probable mechanisms of accumulation of

Figure 11. Dependence of yield strength σy, factors of variation v of yield strength σy, strength δи, and elongation δ<sup>k</sup> from the

8 >><

>>:

The abovementioned basic calculated dependencies in equations (1)–(26) allow [1, 3–7, 18–20] to make the transition from traditional deterministic engineering calculations of strength with the standard characteristics of mechanical properties σy, σ<sup>и</sup> to calculations of strength, durability, crack resistance, reliability, and safety using new developing statistical and probabilistic

Ultimately, the problems of functional and strength reliability, resource, and safety of pipeline systems should cover all stages of the life cycle of facilities, representing three interrelated and

Designing while taking into account the prospects of statistical and probabilistic modeling of reliability and safety criteria should include the development and coordination of the technical

Fвf g Kð Þτ ; Tð Þτ ; Qð Þτ ; Фð Þτ ;

(26)

Fpf g σ τð Þ;еð Þτ ; Fnf g dð Þτ ; lð Þτ ,

damage dð Þτ , and nucleation and development of defects lð Þτ .

ð Þ<sup>τ</sup> ; Poð Þ<sup>τ</sup> � � <sup>¼</sup>

interdependent processes: design, construction, and operation.

methods of mathematical and physical modeling and refined calculations.

The main design parameters will be determined under:

<sup>σ</sup>иð Þ<sup>τ</sup> ; <sup>σ</sup>yð Þ<sup>τ</sup> ; So

8. Conclusion

rolled thickness δ.

100 Probabilistic Modeling in System Engineering

Yuriy V. Lisin<sup>1</sup> , Nikolay A. Makhutov<sup>1</sup> , Vladimir A. Nadein<sup>2</sup> \* and Dmitriy A. Neganov<sup>1</sup>

\*Address all correspondence to: vladimir\_nadein@ogsed.ru

