Model of Cold Standby Parallel System with General Distribution of Failures Times

摘要

The aim of the paper is to develop a model of a 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 fast 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. Semi-Markov and some other models lead to the necessity of compiling and solving systems of integro-differential equations. The authors' approach consists in drawing up an open scheme for the functioning system. As a result of 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. Calculation of residual durations is a feature of the model in question, which, along with detailed schematization, makes it possible to calculate a set of state indicators and, on their basis, obtain the more general indicators of the system functioning that are of interest. A numerical example is given for a system consisting of five devices. Analysis was carried out for the different reliability of the standby device, which is compared both with the operating time of the system before the first failure, and with the time tw.