Assessing the reliability of a surveying and geodetic network based on a Markov model

Purpose. To build a graph of states and transitions of the surveying-geodetic network (SGN), which includes 16 points. To study the functioning of constructed discrete-continuous stochastic Markov models of the surveying-geodetic network with full and current recovery. To perform a numerical calculation of reliability, safety and efficiency indicators: readiness ratio, limit probability states, mean time to failure, mean time between failures. Methodology. A model of SGN functioning is built in the form of a graph of states and transitions with current and full recovery. Based on the model in the Mathcad software, the availability factor, mean time to failure, mean time between failures are calculated. The following graphs are built: readiness functions, probabilities of operation until the first failure, and frequency of getting into an emergency situation. Findings. Constructed discrete-continuous stochastic Markov reliability models of the boundary probability states, mean time between failures, mean time to the first failure have been analyzed. The probability of fault-free operation is presented graphically in the form of a transition graph, which describes the logic of the operation of the SGN. Based on the graph of states and transitions (graphical model) according to the Kolmogorov-Chapman algorithm, an analytical model of the reliability behavior of the surveying-geodetic network was built. A system of linear Kolmogorov-Chapman differential equations was compiled and solved. The distribution of probabilities of being in each state of the surveying-geodetic network has been obtained. Originality. For the first time in surveying practice, a reasonable choice of a discrete-continuous stochastic model of the functioning of a surveying-geodetic network based on the application of the state space method has been made. This model most fully describes the process of functioning (behavior) of the dynamic system. Dependencies between reliability indicators and safety indicators are established. It is recommended to use a model with ongoing network recovery, which allows you to maintain a given level of reliability through timely maintenance (recovery). Practical value. The most expedient time for restoration of geodetic points with certain failure intensity parameters has been determined. It has been done in order to maintain the SGN in an operational state with a given level of reliability. Current network recovery makes it possible to maintain reliability at the desired level. In the case of complete restoration of the SGN, the readiness factor will be lower, but such a system will be significantly cheaper.