Reliability Evaluation of Reverse Osmosis System in Water Treatment Using Modified Weibull Distribution

Maihulla, Anas; Yusuf, Ibrahim; Abdullahi, Ibrahim

doi:10.22034/IJRRS.2023.6.1.6

Reliability Evaluation of Reverse Osmosis System in Water Treatment Using Modified Weibull Distribution

Document Type : Original Research Article

Authors

Anas Maihulla ¹

Ibrahim Yusuf ²

Ibrahim Abdullahi ³

¹ Department of Mathematics, Faculty of Science, Sokoto state University, Sokoto. Nigeria

² Department of Mathematical Sciences,Bayero University, Kano, Nigeria

³ Department of Mathematics, faculty of Science, Sokoto State University, Sokoto, Nigeria

10.22034/IJRRS.2023.6.1.6

Abstract

Recently, reliability has become a critical criterion for product quality and decision-making that covers a wide range of subjects, including failure analysis systems. Performing a reliability analysis is essential for the study of operating safety in industrial systems. In this study, we list evaluation methods and perform real-time reliability analyses. The real-time reliability modeling of a Reverse Osmosis system is addressed in this paper. The model will help create effective maintenance while extending the subsystems' lifespan. To achieve our goal, we suggested the 2-parameter modified Weibull distribution. The simulation was performed using Maple software. The evaluation for each subsystem was displayed in the result and analyses section. The conclusion, however, draws a broad conclusion about the study.

Keywords

Reliability

System

Dependability

Weibull

Reverse Osmosis

parameters

Subjects

Reliability Engineering

Weibull, “A statistical distribution function of wide applicability,” Journal of Applied Mechanics, vol. 18, no. 3, pp. 293–297, Sep. 1951, doi: https://doi.org/10.1115/1.4010337
W. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families,” Biometrika, vol. 84, no. 3, pp. 641–652, Sep. 1997, doi: https://doi.org/10.1093/biomet/84.3.641
Zhang and M. Xie, “On the upper truncated Weibull distribution and its reliability implications,” Reliability Engineering & System Safety, vol. 96, no. 1, pp. 194–200, Jan. 2011, doi: https://doi.org/10.1016/j.ress.2010.09.004
Renou, J. G. Givaudan, S. Poulain, F. Dirassouyan, and P. Moulin, “Landfill leachate treatment: Review and opportunity,” Journal of Hazardous Materials, vol. 150, no. 3, pp. 468–493, Feb. 2008, doi: https://doi.org/10.1016/j.jhazmat.2007.09.077
S. Maihulla and I. Yusuf, “Reliability modeling and performance analysis of reverse osmosis machine in water purification using Gumbel–Hougaard family copula,” Life Cycle Reliab. Saf. Eng., vol. 12, no. 1, pp. 11–22, 2023, doi: https://link.springer.com/article/10.1007/s41872-022-00214-2
S. Maihulla, I. Yusuf, and S. I. Bala, “Performance Evaluation of a Complex Reverse Osmosis Machine System in Water Purification using Reliability, Availability, Maintainability and Dependability Analysis,” Reliability: Theory & Applications, vol. 16, Jan. 2021, [Online]. Available: https://cyberleninka.ru/article/n/performance-evaluation-of-a-complex-reverse-osmosis-machine-system-in-water-purification-using-reliability-availability/pdf.
Billinton and R. N. Allan, Reliability evaluation of engineering systems. 1992. doi: https://doi.org/10.1007/978-1-4899-0685-4
Gupta and P. C. Tewari, “Simulation modeling and analysis of a complex system of a thermal power plant,” DOAJ (DOAJ: Directory of Open Access Journals), Sep. 2009, doi: http://dx.doi.org/10.3926/jiem.2009.v2n2.p387-406
Narahari and N. Viswanadham, “Transient analysis of manufacturing systems performance,” IEEE Transactions on Robotics and Automation, vol. 10, no. 2, pp. 230–244, Apr. 1994, doi: https://doi.org/10.1109/70.282547
Gupta, A. K. Lal, R. K. Sharma, and J. Singh, “Analysis of reliability and availability of serial processes of plastic‐pipe manufacturing plant,” International Journal of Quality & Reliability Management, vol. 24, no. 4, pp. 404–419, Apr. 2007, doi: https://doi.org/10.1108/02656710710740563.
Kaur, A. K. Lal, S. S. Bhatia, and A. S. Reddy, “Numerical solution of stochastic partial differential difference equation arising in reliability engineering,” Applied Mathematics and Computation, vol. 219, no. 14, pp. 7645–7652, Mar. 2013, doi: https://doi.org/10.1016/j.amc.2013.01.052
-J. Wen, X. Liu, and X. Cheng, “Parameter Evaluation of 3-parameter Weibull Distribution based on Adaptive Genetic Algorithm,” in Proceedings of the 2017 2nd International Conference on Machinery, Electronics and Control Simulation (MECS 2017), 2017, doi: 10.2991/mecs-17.2017.78.
Y. Algamal and G. Basheer, “Reliability Estimation of Three Parameters Weibull Distribution based on Particle Swarm Optimization,” Pakistan Journal of Statistics and Operation Research, pp. 35–42, Feb. 2021, doi: https://doi.org/10.18187/pjsor.v17i1.2354
T. Quek, Structural system reliability by the method of stable configuration. University of Illinois at Urbana-Champaign, 1987.
L. Rohde, G. Jain, A. K. Poddar, and A. Ghosh, Introduction to differential calculus: systematic studies with engineering applications for beginners. John Wiley & Sons, 2012.
W. Momber, Hydrodemolition of concrete surfaces and reinforced concrete structures. Elsevier, 2005, pp. xiii, 269 p. [Online]. Available: http://ci.nii.ac.jp/ncid/BA77134830?l=en.
T. Walker, Ed., Decontamination in hospitals and healthcare, 2nd ed. Cambridge, England: Woodhead Publishing, 2019.
S. Maihulla and I. Yusuf, “Reliability and performance prediction of a small serial solar photovoltaic system for rural consumption using the Gumbel-Hougaard family copula,” Life Cycle Reliability and Safety Engineering, vol. 10, no. 4, pp. 347–354, Nov. 2021, doi: https://doi.org/10.1007/s41872-021-00176-x
G. Easterling, "Discussion of: Confidence Interval Estimation for the Weibull and Extreme Value Distributions," Technometrics, vol. 20, no. 4, pp. 365-368, 1978, doi: https://doi.org/10.2307/1267634.
A. Thompson, Journal of the American Statistical Association, vol. 78, no. 382, pp. 507-508, 1983, doi: https://doi.org/10.2307/2288691.
M. Soland, “Bayesian analysis of the WEIBUll process with unknown scale and shape parameters,” IEEE Transactions on Reliability, vol. R-18, no. 4, pp. 181–184, Nov. 1969, doi: https://doi.org/10.1109/TR.1969.5216348
G. Papadopoulos and C. P. Tsokos, “Bayesian confidence bounds for the WeiBull failure model,” IEEE Transactions on Reliability, vol. R-24, no. 1, pp. 21–26, Apr. 1975, doi: https://doi.org/10.1109/TR.1975.5215319
Dellaportas and D. Wright, “Numerical prediction for the Two-Parameter WeIBull distribution,” The Statistician, vol. 40, no. 4, p. 365, Jan. 1991, doi: https://doi.org/10.2307/2348725
R. Mann, “Point and interval estimation procedures for the Two-Parameter WEIBull and Extreme-Value distributions,” Technometrics, vol. 10, no. 2, pp. 231–256, May 1968, doi: https://doi.org/10.1080/00401706.1968.10490558
S. Maihulla and I. Yusuf, “Performance Analysis of Photovoltaic Systems Using (RAMD) Analysis,” J. Nig. Soc. Phys. Sci., pp. 172–180, Aug. 2021, doi: https://doi.org/10.46481/jnsps.2021.194
Tabrizi and M. Rahmani, "Assessment of Reliability and Availability of a Photovoltaic Power Plant," presented at the Conference: First National Conference of Optimization in Renewable Energies, 2021.