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This paper proposes the study of modelling and analysis of a two unit parallel system. A constant failure rate is considered for the units which are identical in nature. All repair activities like repair, replacement, preventive maintenance are mended immediately by a single server. The repair of the unit is done after its failure and if the fault is not rectified by the server within a given repair time, called maximum repair time, the unit replaced by new one. And, if there is no fault occurs up to a pre-fixed operation time, called maximum operation time, the unit undergoes for the preventive maintenance. The unit works as new after all repair activities done by the server. Priority to repair of one unit is given over the replacement of the other one. All random variables are statistically independent. The distribution for the failure, preventive maintenance and replacement rates are negative exponential whereas the distribution for all repair activities are taken as arbitrary with different probability density functions. Semi-Markov and regenerative point techniques are used to derive some reliability measures in steady state. The variation of MTSF, availability and profit function has been observed graphically for various parameters and costs. Reetu Rathee | S. C. Malik | D. Pawar"Reliability Modeling and Analysis of a Parallel Unit System with Priority to Repair over Replacement Subject to Maximum Operation and Repair Times" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018, URL: http://www.ijtsrd.com/papers/ijtsrd15655.pdf http://www.ijtsrd.com/mathemetics/statistics/15655/reliability-modeling-and-analysis-of-a-parallel-unit-system-with-priority-to-repair-over-replacement-subject-to-maximum-operation-and-repair-times/reetu-rathee