# Modeling Complex Technical Systems Operation Processes

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## Abstract

The operation process of a complex technical system is considered and its operation states are introduced. The semi-Markov process is used to construct a general probabilistic model of the considered complex technical system operation processes. To build this model the vector of probabilities of the system operation process stay at the initial operation states, the matrix of probabilities of the system operation process transitions between the operation states, the matrix of conditional distribution functions and the matrix of conditional density functions of the system operation process conditional sojourn times at the operation states are defined. To describe the system operation process conditional sojourn times at the particular operation states the uniform distribution, the triangular distribution, the double trapezium distribution, the quasi-trapezium distribution, the exponential distribution, the Weibull distribution and the chimney distribution are suggested and introduced. Under all these assumptions from the constructed model, the main characteristics of the system operation process are found. The mean values of the system operation process conditional sojourn times at the particular operation states having these distributions are given. Moreover, the distribution functions of the system operation process unconditional sojourn times at the particular operation states, the mean values of the system operation process unconditional sojourn times at the particular operation states, the limit values of the transient probabilities of the system operation process at the particular operation states and the approximate mean values of the system operation process total sojourn times at the particular operation states for the fixed sufficiently large system operation time are determined. Applications of the proposed model for the evaluation and prediction of the operation processes’ characteristics of the exemplary system, the port oil transportation system and the maritime ferry technical system, are presented as well.

## Keywords

Operation State Operation Process Sojourn Time Technical System Triangular Distribution## References

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