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operating stresses not exceeding 0.5 of the strength level of the composite material, the reliability of MCOPV is ensured at a level of at least 0.999 at the end of operation time in orbit. When the relative stresses level is increased to 0.6, high reliability is ensured only in the first 500 h of

Leakage breach of liner in the test 1.3 <sup>10</sup><sup>6</sup> 1.1 <sup>10</sup><sup>6</sup>

at the beginning work 1.1 <sup>10</sup><sup>8</sup> 2.5 <sup>10</sup><sup>9</sup> at the end work 2.8 <sup>10</sup><sup>7</sup> 6.3 <sup>10</sup><sup>8</sup>

at the beginning work 2.4 <sup>10</sup><sup>8</sup> 4.7 <sup>10</sup><sup>9</sup> at the end work 1.8 <sup>10</sup><sup>6</sup> 3.7 <sup>10</sup><sup>7</sup>

7-layer shell 9-layer shell

Quantitative risk assessments were performed for the most dangerous scenarios. The risk calculation was performed for the time moments 1000 h (the beginning work on the orbit) and 15,000 h (at the end work on the orbit). The calculation of the risk fracture of MCOPV was carried out according to the Phoenix approach, replacing the standard fracture stress of the composite σ<sup>f</sup> by the numerical or experimental estimate of the actual value of the composite

The results of the calculation are presented in the Table 1. The obtained risk assessments can be regarded as tentative, since they do not take into account possible processes of creep of liner and composite under load during the MCOPV operation. It should be noted that obtained values of the probabilities of destruction of the MCOPV belong to the class of extremely unlikely events. Therefore, the risk of destruction of the MCOPV in the orbit can be considered

This chapter provided some aspects to probabilistic modelling in solving analytical problems of system engineering. The main tasks of engineering design are analysis of system operation from the moment of the conception and substantiation of the initial idea to the moment of writing off and wrapping the product so that it does not fail during the service period. When solving these problems, variability in the employed materials, loads, manufacturing process, testing techniques, and application inevitably arise. Probabilistic models and probabilistic methods proceed from the fact that various uncertainties are inevitable end essential features of the nature on an engineering system or design and provide ways of dealing with quantities whose values cannot be predicted with absolute certainty. Unlike deterministic methods,

operation. The load level of more than 0.6 is unacceptable for the MCOPVs.

Type of destruction Risk fracture of MCOPV

Leakage breach of liner in the space (orbit)

20 Probabilistic Modeling in System Engineering

Table 1. Calculated estimates of risk fracture of MCOPV.

Fracture of MCOPV in the space

strength σc.

acceptable.

4. Conclusion

Anatoly Lepikhin<sup>1</sup> \*, Vladimir Moskvichev<sup>1</sup> and Nikolay Machutov<sup>2</sup>

