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The aim of this paper is to develop a probabilistic model for a cold standby system that consists of an imperfect switching device and a servicing facility. The model aims to address the issue of unexpected random failures of the switch by implementing preventive maintenance measures. The system has two identical units. It starts with one unit in active operation and another unit in cold standby mode. In standby mode the unit remains in perfect state. No failure is allowed in standby mode. As the operating unit fails, the standby unit needs to be switched into operation, to keep the system working. A servicing facility is present in the system to perform necessary servicing related tasks. The servicing facility referred to as the server, also takes care of all necessary remedial activities like preventive maintenance and repairs. The switch used as switching mechanism to place the standby unit into operation may found imperfect when needed. Similarly, the server too can fail while doing job. A preventive maintenance scheme is used for the switch whereas treatment is given to server. The method of semi-Markov process and regenerative point technique is used for model developing and solving, respectively. The expressions are derived to determine different system performance measures such as mean time to system failure, availability, busy period, expected number of preventive maintenances and the profit. The distributions of random time elapsed in repairs, replacements, preventive maintenances and treatments are general. This study highlights the usefulness of switch's preventive maintenance in long run. To study the asymptotic behavior of the system model, all the expressions for system performance measures are obtained in steady state. A simulation study is conducted using a presumed data set and assuming a Weibull probability distribution. The numerical results are shown in tabular form. The simulation results serve to highlight the significance of preventive maintenance for the switch. The findings of the paper can provide guidelines to the people engaged in designing, framing and implementing standby switching systems in real applications. [ABSTRACT FROM AUTHOR]

The complexity of engineering systems makes it challenging to keep them functional without failures for longer interval of time. This task is achieved by adopting effective maintenance strategies and appropriate structure design. So in such cases the functioning of service mechanism and chat of the server becomes essential. The server failure during any maintenance activity may lead to declined availability and hence the profit. In this paper we develop a probabilistic model for a standby system consisting of two identical units and a server subject to failure and treatment. The inspection of failed server reveals feasibility for treatment or replacement. The replacement time of server and switching time of standby is negligible. The failure, repair, inspection and treatment times are assumed as arbitrary. The model is developed using semi-Markov process and the steady state results of interests are derived using regeneration point technique of renewal theory and Laplace transfornations. The practical importance of the study is highlighted through numerical simulation, for a particular case. [ABSTRACT FROM AUTHOR]