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AM> Vol.6 No.2, February 2015
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Availability and Profit Optimization of Series-Parallel System with Linear Consecutive Cold Standby Units

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DOI: 10.4236/am.2015.62032    3,947 Downloads   4,471 Views   Citations
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Muhammad Sagir Aliyu1, Ibrahim Yusuf2, U. A. Ali1


1Department of Mathematics, Usmanu Dan Fodio University, Sokoto, Nigeria.
2Department of Mathematical Sciences, Bayero University, Kano, Nigeria.


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.


Availability, Profit, Cold Standby, Optimization

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Aliyu, M. , Yusuf, I. and Ali, U. (2015) Availability and Profit Optimization of Series-Parallel System with Linear Consecutive Cold Standby Units. Applied Mathematics, 6, 332-344. doi: 10.4236/am.2015.62032.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Hu, l., Yue, D. and Li, J. (2012) Availability Analysis and Design Optimization for a Repairable Series-Parallel System with Dependencies, International Journal of Innovative Computing, Information and Control, 8, 6693-6705.
[2] Khatab, A., Nahas, N. and Nourelfath, M. (2009) Availbilty of K-Out-of-N: G Systems with Non-Identical Components Subject to Repair Priorities. Reliability Engineering & System Safety, 94, 142-151.
[3] Krishnan, R. and Somasundaram, S. (2012) Reliability and Profit Analysis of Repairable K-Out-of-N System with Sensor. European Journal of Scientific Research, 67, 215-222.
[4] Juang, Y.-S., Lin, S.-S. and Kao, H.-P. (2008) A Knowledge Management System for Series-Parallel Availability Optimization and Design. Expert Systems with Applications, 34, 181-193.
[5] Levitin, G. (2002) Optimal Series-Parallel Topology of Multi-State System with Two Failure Modes. Reliability Engineering & System Safety, 77, 93-107.
[6] Li, C.Y., Chen, X., Yi, X.S. and Tao, J.Y. (2010) Heterogeneous Redundancy Optimization for Multi-State Series-Parallel Systems Subject to Common Cause Failures. Reliability Engineering and System Safety, 95, 202-207.
[7] Wang, S. and Wadata, J. (2009) Reliability Optimization of a Series-Parallel System with Fuzzy Random Lifetimes. International Journal of Innovative Computing, Information and Control, 5, 1547-1558.
[8] Wang, K.H. and Chen, Y.J. (2009) Comparative Analysis of Availability between Three Systems with General Repair Times, Reboot Delay and Switching Failures. Applied Mathematics and Computation, 215, 384-394.
[9] Wang, K.-H., Yen, T.-C. and Fang, Y.-C. (2012) Comparison of Availability between Two Systems with Warm Standby Units and Different Imperfect Coverage. Quality Technology and Quantitative Management, 9, 265-282.

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