In an automobile engine, the heat transfer cannot be possible without cooling system support. The cooling system has a great importance in the engines. It coolants overheat of the engine, and prevents it from breakdown, that's why a highly reliable cooling system is the necessity of every engine but there are many failure issues with a cooling system which are time dependent. This paper investigates the performance of a water cooling system with the consideration of their significant components by taking the attention of three types of time dependent failure issues while the water cooling system is maintained by the sufficient repair facility. It is obvious that in the lack of maintenance, failure issues in water cooling system lead with the increment of time. Maintenance and operating costs of water cooling system affect the economy of overall engine very much, so, it is necessary to be aware about overheating of engines during peak ambient conditions when it is operated with full capacity. Hence, a Mathematical model of water cooling system is proposed by using the Markov process and supplementary variable technique.

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