Model of unreliable devices system

Abstract

The purpose of the research is to develop a model of a production system consisting of n parallel devices and having a standby device of lower reliability. Under complex failure conditions, a spare device in a cold standby allows quickly replacing the failed primary unit. The system operation is investigated from the beginning of work up to a certain point in time tW. A good approximation to reality is the acceptance that failure time follows general time distribution. The authored approach consists in drawing up an open scheme for the functioning system. Due to the complex failure of one of the devices, the process passes to the next state, which is characterized by residual failure time or residual time of the process. The calculation of residual durations is a feature of the investigated model, which, along with detailed schematization, makes it possible to calculate the set of state indicators and, on their basis, obtain the more general indicators of the functioning of investigated system. A numerical example is given for a system consisting of five devices.