CONSTRUCTION OF GEODESIC NETWORKS ON THE BASIS OF THE THEORY OF MARKOV ACCIDENTAL PROCESSES AND THE THEORY OF RELIABILITY
Authors: Gladilin Valeriy , Siroshtan Tatiana , Gamalij Irina , Shudra Nataliia , Chulanov Petro 
Published: September 2022

As mentioned above, the theory of reliability was mainly developed for technical devices. However, nowadays it is widely used in construction, and is also beginning to be used in geodesy. By abstracting its position can be successfully transferred to systems that do not seem to be in a dynamic state. Take, for example, the polygon metric network in the city. It would seem that such a network is in a static state, but over time it undergoes changes, ie it is in subtle dynamics and its reliability is gradually declining.

Reliability in the broadest sense of the word means the ability of a technical device (system, network) to uninterrupted (trouble-free) operation for a specified period of time under certain conditions. This period of time is usually due to the time of a task. Which is carried out by a device or system and is part of the overall operational task.

Currently, the problem of reliability is becoming one of the key problems of technology and management. Ensuring the reliable operation of all elements of the system is of paramount importance.

Improving reliability requires special study and quantitative analysis of the phenomena associated with accidental failures of devices or systems. At this time, the theory of reliability has become a special science that makes extensive use of probable methods of examination.

In the theory of reliability there are two types of failures: sudden and gradual. Consider sudden failures. Sudden device failures are understood as an instantaneous failure, which means that it cannot be used, and these failures occur at some random point in time.

The reliability of the system depends on the composition and number of elements included in it, on the type of integration into the system and on the characteristics of each individual element. An element is to be understood as any device that is not subject to further disconnection, the reliability of which is specified or determined experimentally. By assembling such elements in different ways into systems, we will solve the problem of determining the reliability of the system depending on the reliability of its elements.

The reliability of elements and systems is determined by numerical characteristics. We give some definitions of these characteristics for the element and the system as a whole.

The reliability of the element is the probability that the element in certain conditions will work flawlessly over time, its probability is denoted. With increasing time, reliability usually decreases; with probability.

In the geodetic literature, the term "reliability" is often used, which means the accuracy of the obtained results of geodetic measurements. However, the reliability of a geodetic sign or network as a whole, from the point of view of reliability theory should be considered, for example, the ability of a sign or network to survive on the ground without changing location (without changing spatial coordinates) for a given period of time under certain conditions. In other words, the reliability of a geodetic sign or network as a whole is the probability that the sign or network in these conditions will fail to "work" until the end of a given time.