Profit Analysis of RANR Systems

This paper studies a system with repairable and non-repairable failures. When the system is operating, it is inspected once every random time to make sure whether it is normal or abnormal until it attains a failure mode, or until the result of the inspection shows the system is abnormal. By using probability analysis, definite integral, Laplace transform and the supplementary variable technique, this paper gets the mean profits per unit time generated by the system from starting construction of the system to entering a non-repairable failure mode, which is called the profit function of the system. As an application of the function, the optimal inspection policy of the system is also studied.