Profit analysis of a warm standby non-identical unit system with single server performing in normal/abnormal environment

Abstract

A system/unit is called working in normal environment if it is operating within prescribed conditions set by the manufacturer, otherwise the system is called working in abnormal environment. For example; a hydraulic machine having capacity uplifting the weight of 500 tons exceeds its capacity is termed as working in abnormal environment conditions. In this paper, profit analysis of a warm standby non-identical unit system with single server subject normal/abnormal environment conditions has been discussed. There is a single server who is allowed to do job in normal weather condition only and while performing its job it adopts FCFS (first come first serve) policy. The system model consists of two non-identical units—one is operative and the other kept as warm standby. The main unit may fail directly from normal mode, while failure of warm standby unit takes place owing to remaining unused for a longer period of time. The time taken for repair activity by the server follows negative exponential distribution. The expressions of various reliability measures are analyzed in steady state using semi-Markov process and regenerative point technique. Also, take the arbitrary values for the parameters (i.e., λ, μ, ϕ and θ) to delineate the behavior of some important performance measures to check the efficacy of the system model under such situations shown in the graphs.