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# Profit Analysis of a Two Unit Cold Standby System Operating Under Different Weather Conditions Subject t o Inspection

## Abstract

A system, or unit, is said to be working under normal weather conditions if the system is working under prescribed conditions as defined/stated by the definition of reliability of system/unit, otherwise the system is said to be working in abnormal weather conditions. For example, if a car with the capacity for five persons is carrying more than five persons, it will be said to be working under abnormal weather conditions. Another example, if a hydraulic machine having the capacity to lift a maximum weight of 500 tons is lifting a weight of 600 tons, then the machine is working under abnormal weather conditions. Hence, in this situation, work done by the machine is out of its capacity and the machine is working in abnormal weather conditions. If the machine is working within the capacity of the stated conditions, it is said to be working in normal weather conditions. The main purpose of this paper is to analyze the profit of a two-unit system called the standby system that is working under different weather conditions in an inspection facility. There is a single perfect server who visits the system immediately whenever required. A server inspects the unit before repair/replacement of the failed unit. All the mechanical activities done by the server are only possible during normal weather conditions. There are two possibilities after inspection of the unit; either repair of the unit is feasible or not feasible. If repair of the unit is not feasible, then the unit will be replaced immediately by a new unit. Otherwise, the repaired unit works as a new unit. The operative unit undergoes preventive maintenance after a specific (maximum) operation time. All random variables are statistically independent. The failure rate and the rate by which the system undergoes for preventive maintenance are constant whereas the inspection rate, repair rate, and maintenance rate follow negative exponential distributions. The expressions for several reliability measures are derived in steady state conditions using the regenerative point technique and semi-Markov process. The graphical behavior of MTSF, availability and profit function, has been depicted with respect to preventive maintenance rate for arbitrary values of other parameters and costs.

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