Availability and Profit Optimization of Series-Parallel System with Linear Consecutive Cold Standby Units
- 1 Department of Mathematics, Usmanu Dan Fodio University, Sokoto, Nigeria
- 2 Department of Mathematical Sciences, Bayero University, Kano, Nigeria
- 3 Department of Mathematics, Usmanu Dan Fodio University, Sokoto, Nigeria
Abstract
In this paper, we study availability and profit optimization of a series-parallel system consisting of three subsystems A , B and C in which A and B are cold standby. Subsystem A consists of linear consecutive k -out-of- n units while subsystems B and C consist of a single unit each. The system works if any of A or B and C work. The objective of this study is to maximize the steady-state availability and profit. To solve the optimization problem, different numbers of units for n = 2, 3, 4, 5 in subsystem A are considered. Explicit expressions for busy period of repairmen, steady-state availability and profit function are derived using linear first order differential equations. Several cases are analyzed graphically for n = 2, 3, 4, 5 to investigate the effects of various system parameters on availability and profit. The paper also presents graphical comparison for specific values of system parameters and finds that the optimal system configuration is when n = 5.
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