Abstract
Abstracts The dynamic model of change in the performance indicators of sophisticated equipment was proposed. The proposed model consists of two parts. The first part concerns modeling of a random process of changes in the level of equipment loading and is described by the stochastic equation in the form of Ito (5). The second part concerns modeling of dynamics of equipment wear depending on changing in the levels of its loading and is described by the differential equation. As a result, the stochastic dynamic model of changes in performance indicators of sophisticated equipment, which takes into account random fluctuations of equipment loading, was obtained. Using the proposed model, we analyzed dynamics of average total specific costs of equipment in the case when a degree of equipment loading is subject to random changes. Quantitative ratios of average total specific costs of equipment, level of fluctuations of these costs during possible random changes in loading and terms of equipment replacement were established. Studies have demonstrated that changes in average total specific costs of equipment can be insignificant for a certain time. In this case, the spread range of the level of costs of equipment within the same time range can increase significantly. That is why it makes sense to reduce the service term of equipment. This would lead to an insignificant increase in the mean values of equipment performance indicators, however, their stability level will improve considerably.
Highlights
The second part concerns modeling of dynamics of equipment wear depending on changing in the levels of its loading and is described by differential equation (10) and formulas (11)–(14)
We obtained the stochastic dynamic model of a change in performance indicators of sophisticated equipment (1)– (20), which takes into account random fluctuations in the level of equipment loading
It was proposed to determine a random process of changing the level of equipment loading, described by the stochastic model of state in the form of Ito (5), with the use of displacement function (1) and diffusion function (3)
Summary
Operational characteristics of equipment tend to worsen due to ageing and wear. Physical wear leads to an increase in the number of breakdowns and increases in current expenditures for equipment. Article [7] examines the issue about making decisions on the replacement of chains of machines over time employing an optimal control model, which takes into account random factors of machines’ failures. Studies [8, 9] tackled the issues of coordination of operations on maintenance equipment with the investment strategies in the presence of possible random failures of equipment In these works, in contrast to the traditional approach, which was proposed in the classic paper [3], a stochastic process of failures of machines is modeled explicitly. In the studies given above, various options for stating the problem on the substantiation of terms of equipment replacement are proposed, employing different methods and models aimed at resolving it. All of them fail to establish quantitative relationships between the average level of equipment efficiency indicators, the level of fluctuations in these indicators at possible random fluctuations in loading and the term of equipment replacement
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