Stochastic Analysis of a Three-Unit Non-Identical Repairable System with Simultaneous Working of Cold Standby Units

Here, stochastic analysis of a repairable system of three units has been carried out by taking one unit in operation (called main unit) and two identical units (called duplicate units) in cold standby. The switch device is used to convert the standby units into operative mode. A single server is hired to handle repair activities of the units who visits the system instantly whenever needed. The repair done by the server is perfect and thus the repaired unit follows the same lifetime distribution as the original. The constant failure rates are considered for both main and the duplicate units while their repair time distributions are taken as arbitrary. Some important reliability measures including mean sojourn times (MST), transition probabilities (TP), mean time to system failure (MTSF), availability, expected number of repairs for both kinds of units separately, expected number of visits by the server and busy period analysis of the server due to repair are determined using semi-Markov process (SMP) and regenerative point technique (RPT). The arbitrary values of the parameters are considered to examine the behaviour of some significant reliability measures through graphs. The possible application of the system model can be visualized in a power supply system of a house where a set of solar panels are kept in spare for their simultaneously working when main power supply is discontinued.