Profit Analysis of a Repairable System with Imperfect Coverage and Service Pressure Coefficient

We consider the warm-standby M/M/R machine repair problem with multiple imperfect coverage which involving the service pressure condition. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced with a coverage probability c by a standby if one is available. Using the recursive method, we develop the steady-state solutions which are used to calculate various system performance measures. We develop the expected profit function per unit time to determine the joint optimal values at the maximum profit. We first use the direct search method to find the optimal number of servers R and the optimal number of warm standby S. Subsequently, we apply the Quasi-Newton method to obtain the optimal service rate μ* and the optimal coverage probability c* after R* and S*are fixed. Finally, we perform a sensitivity analysis to study the effects on the optimal values ( R*, S*, μ*, c* ) if the system parameters take on other specific values.