Mathematical model for reliability assessment of device for preparation and distribution of animal feed as “Man-Machine”

Raising the reliability of machines for preparation and distribution of feed in animal husbandry is an urgent scientific and practical task. The purpose of the work is to develop a mathematical model of reliability of a technical system “Man-Machine” (using as an example machines for preparation and distribution animal feed) in order to identify the influence of its main components upon the dynamic characteristics with a gradual loss of its initial parameters. The model is described by Holmogorov’s stochastic differential balance equations of probabilities of states and transitions. The system of equations was solved in Laplace transformations. The probabilities of states in the form of transitions from originals to images were found according to Cramer’s rule. Under extreme conditions at the start of the operation and under the conditions of a settled pseudo-static mode during long-term operation of the systems, a readiness function was obtained that corresponds to the physical essence of the systems’ operable state. With an increase in the time of operation of the “man-machine” system its readiness for work under the conditions of “aging” of the equipment and increasing the operators’ fatigue decreases asymptotically, approaching its finishing value. It has been established that the optimal value of the probability of failure-free operation within the range of 0.92–0.98 corresponds to 350–500 hours of operation of the device for preparation and distributing feed. The probability of non-failure operation of the “human operator” has a higher value compared to the probability of non-failure operation of the “machine”. Within the indicated operating time the probability of failure-free operation is respectively: for the “machine” – 0.84–0.89; for the “human operator” – 0.93–0.98.