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# Mathematical modeling of the reliability of a solar hot water system in the Republic of Mari El

Abstract

### Mathematical modeling of the reliability of a solar hot water system in the Republic of Mari El

Kamenskih A.D., Medyakov A.A., Ostashenkov A.P., Sozonov K.A.

Incoming article date: 17.12.2019

The reliability of the solar heating system with solar collectors was studied using the logical-probabilistic method by building a fault tree. The fault tree was obtained by sequentially detailing the events associated with failures of the solar heating system, as well as its elements. Events were taken into account: conducting test diagnostics of elements of the power supply system, repairing failed elements, failure of elements, reducing the power of solar collectors due to a decrease in the intensity of the solar radiation. The events were divided into two groups: events in which there is sufficient intensity of solar radiation for the hot water supply from the solar collectors, as well as events when the heating supply cannot be provided only due to the solar collectors. The last group of events was divided into two subgroups, within events caused short-term downtimes (at the time of switching) and long-term downtimes (at the time of replacing or repairing a failed system element). Long shutdowns are associated with the coincidence of failures, repair or diagnosis of one or more elements of the solar heating system. Expressions are compiled to calculate the probability of long downtimes, the probability of short downtimes, the probability of failure due to a decrease in the intensity of the solar radiation, and the total probability of failures. As a result of substituting the values of the reliability indicators of the elements of the solar heating system, the value of the total probability of failure during the year is 4.03∙10-5.

Keywords: solar hot water supply, reliability, solar collector, failure cause, reliability modeling