A general model of industrial systems operation processes related to their environment and infrastructure

The operation process of the complex industrial 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 industrial system operation process. To build this model the vector of probabilities of the system operation process initials 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 in the operation states are defined. To describe the system operation process conditional sojourn times in the particular operation states the uniform distribution, the triangle distribution, the double trapezium distribution, the exponential distribution, the Weibull distribution and the normal distribution are suggested. Under these all assumptions from the constructed general model the main characteristics of the system operation process are find. The mean values of the system operation process conditional sojourn times in particular operation states having these distributions are calculated. Moreover, the unconditional distribution functions of the system operation process unconditional sojourn times in the particular operation states, the mean values of the system operation process unconditional sojourn times in the particular operation states, the limit values of the transient probabilities of the system operation process at the particular operation states and the mean values of the system operation process total sojourn times in the particular operation states are determined.