Identification methods and procedures of critical infrastructure operation process including operating environment threats

In the paper, there are presented the methods for identification of the critical infrastructure operation process on the basis of statistical data coming from this process realizations related to the critical infrastructure operating environment threats. These are the methods and procedures for estimating the unknown basic parameters of the critical infrastructure operation process semi-Markov model and identifying the distributions of the critical infrastructure operation process conditional critical infrastructure operation process sojourn times at the particular operation states. There are given the formulae estimating the probabilities of the critical infrastructure operation process straying at the particular operation states at the initial moment, the probabilities of the critical infrastructure operation process transitions between the operation states. Moreover, there are given formulae for the estimator of unknown parameters of the distributions suitable and typical for the description of the critical infrastructure operation process conditional sojourn times at the operation states. Namely, the parameters of the uniform distribution, the triangular distribution, the double trapezium distribution, the quasi-trapezium distribution, the exponential distribution, the Weibull’s distribution and the chimney distribution are estimated using the statistical methods such as the method of moments and the maximum likelihood method. The chi-square goodness-of-fit test is described and proposed to be applied to verifying the hypotheses about these distributions choice validity. The procedure of statistical data sets uniformity analysis based on Kolmogorov-Smirnov test is proposed to be applied to the empirical conditional sojourn times at the operation states coming from different realizations of the same critical infrastructure operation process.