Reliability and Cost Analysis of Sachet Water Plant Using Copula Approach
Subject Areas : Reliability theory
1 - Department of Mathematics, Kano State College of Education and Preliminary Studies
Keywords: reliability, Availability, Sachet Water, serial system,
Abstract :
The goal of this study is to provide an analytical framework for a standby serial sachet water plant. The plant is made up of five subsystems: a storage tank, filters, a tank, boosters, and a production machine, all of which are set up in a series-parallel configuration. The failure rates of both subsystems/units are continuous and supposed to tail exponential function, but repair is categories into the following; general repair for partially failed state while copula repair for complete failed state. A repair person is on-call 24 hours a day, seven days a week to repair failed units in the system. The transition diagram is used to obtain partial differential equations of degree one, which are resolved using supplementary variable procedure, Laplace conversion and MAPLE software, to derive expressions for numerous dependability agencies name; availability, reliability, MTTF, sensitivity MTTF, and cost of the sachet water plant. Arithmetical instances are delivered in order to demonstrate the achieved results and also to investigate the influence of parameters used. Tables and figures revealed that copula repair outperforms general repair in terms of returns.
⎯ Aliyu, M.S., Yusuf, I. and Ali, U.A. (2015). Availability and profit
optimization of series-parallel system with linear consecutive cold
standby unit’, Applied Mathematics, 6(2), 332–344.
DOI:10.4236/am.2015.62032
⎯ Garg, H. (2014). Reliability, availability and maintainability analysis of
industrial systems using PSO and fuzzy methodology. MAPAN, 29(2),
115-129. DOI: 10.1007/s12647-013-0081-x
⎯ Garg, H. (2016). A novel approach for analyzing the reliability of seriesparallel system using credibility theory and different types of intuitionistic fuzzy numbers. Journal of the Brazilian Society of
Mechanical Sciences and Engineering, 38(3), 1021-1035. DOI:
10.1007/s40430-014-0284-2
⎯ Garg, H. (2016). An approach for analyzing the reliability of industrial
system using fuzzy kolmogrov’s differential equations. Arabian Journal
for Science and Engineering, 40(3), 975-987. DOI: 10.1007/s13369-
015-1584-2
⎯ Garg, H. (2017). Performance analysis of an industrial system using soft
computing based hybridized technique,Journal of Brazilian. Society of
Mechanical, Science and Engineering. 39,1441–1451 DOI
10.1007/s40430-016-0552-4
⎯ Gulati, J, Singh,V. V.,Rawal, D.KandGoel, C. K. (2016).Performance
analysis of complex system in the series configuration under different
failure and repair discipline using Gumbel-Hougaard family Copula.
International Journal of Reliability, Quality, and Safety Engineering.
23 (2),1-2.
⎯ Kumar,S., Pant, S., and Singh, S.B. (2018). Assessment of reliability of
a system by applying hesitant fuzzy set. International Journal of Quality
and Reliability Management. 34 (6), 879–894.
⎯ Kassenga, G.R (2007). The Health - Related Microbiological Quality of
Bottled Water Sold in Retail Outlets in Nigerian, In Consumer Affairs
Movement of Nigeria (CAMON), (2004): NAFDAC to Ban Pure Water
-97% Samples Contaminated. Consumer Link 1:1
⎯ Kontagora, N.M. (2010) Analysis of Pure Water production: A case
study of Ten (10) Randomly Selected Pure water firms in Minna Niger
State. Global Journal of Mathematics and Statistics. 2 (2), 153-159.
⎯ Lado, A and V. V. Singh. (2019). Cost Assessment of complex
repairable system consisting two subsystems in Series configuration
using Gumbel Hougaard family copula. International Journal of Quality
Reliability and Management. 36(10), 1683-1698.
⎯ Minner, C.A., Tagurum, Y.O., Hassan, Z., Afolaranmi, T.O., Bello,
D.A., Dakhin, A., and Zoakah, A.I. (2011). Sachet Water: Prevalence of
Use, Perception and Quality in a Community of Jos South Local
Government Area of Plateau State. Jos Journal of Medicine. 8 (3), 12-
16.
⎯ Niwas, R. and Garg, H. (2018). An approach for analyzing the reliability
and profit of an industrial system based on the cost-free warranty policy.
Journal of the Brazilian Society of Mechanical Sciences and
Engineering, 40: 265. DOI: 10.1007/s40430-018-1167-8
⎯ Omalu, I.J.C., Eze, G.C., Olayemi, I.K., Gbesi, S., Ademiran, L.A.,
Ayanwale, A.V., Mohammad, A.Z., and Khukwumeka, V. (2010).
Contamination of Sachet Water in Nigeria: Assessment and Health
Impact. Online Journal Health and Allied Sciences. 9 (4), 125-131.
⎯ Pourhassan MR, Raissi S and Hafezalkotob A. (2020). ‘A simulation
approach on reliability assessment of complex system subject to
stochastic degradation and random shock’. Eksploatacja i
Niezawodnosc – Maintenance and Reliability 22 (2), p 370–379,
http://dx.doi.org/10.17531/ein.2020.2.20
⎯ Pourhassan, MR. Raissi, S and Apornak, A. (2020). ‘Modeling multistate system reliability analysis in a power station under fatal and nonfatal shocks’. International Journal of Quality and Reliability
Management, vol. 38 (10), DOI: https://doi.org/10.1108/IJQRM-07-
2020-0244
⎯ Ram, M., Singh, S.B. and Singh, V.V. (2013). Stochastic analysis of a
standby complex system with waiting repair strategy, IEEE Transactions on System, Man, and
Cybernetics-Part A:System and Humans. 43 (3), 698–707.
⎯ Ram, M and Amit Kumar, A. (2015). Performability analysis of a
system under 1-out-of-2: G Scheme
⎯ with perfect reworking, Journal of Brazilian. Society of Mechanical,
Science and Engineering. 37:1029–1038 DOI 10.1007/s40430-014-
0227-y
⎯ Rawal, D.K., Ram, M. and Singh, V.V. (2014). Modeling and
availability analysis of internet datacenter with various maintenance
policies’, IJE Transactions A: Basics, Vol. 27, No. 4, pp.599–608
⎯ Raissi, S and Ebadi, Sh. (2018). ‘A Computer Simulation Model for
Reliability Estimation of a Complex System’. Spring, Volume 7, Issue
1, Pages 19-31
⎯ Singh, V.V and Rawal, D.K. (2015). Availability, MTTF, and cost
analysis of the complex system under preemptive resume repair policy
using copula distribution, Journal of Statistics and Operation Research
.10 (3), 299–321. DOI:10.18187/pjsor.v10i3.724
⎯ Singh, v. v., Ismail, A. L., Yusuf, I. and Abdullahi, A. H. (2021)
‘Probabilistic Assessment of Computer-Based Test (CBT) Network
system consists of four subsystems in Series Configuration Using
Copula Linguistic Approach’ International journal of Reliability
and Statistical Studies Vol. 13 (2-4), pp. 401-428.
⎯ Yusuf, I., Babagana, M., Yusuf, B. and Lawan, M.A. (2014). Reliability
Analysis of a Linear consecutive 2-out-of-3 System in the presence of
Supporting Device and Repairable Service Station. International
Journal of operation research, 13(1): 013-024. DOI: 10.21307/ijor2016-002
⎯ Yusuf, I. (2016). Reliability Modeling of a Parallel System with a
Supporting Device and Two Types of Preventive Maintenance,
International journal of operational Research. 25 (3), 269-287. DOI:
10.1504/IJOR.2016.074754
⎯ Yusuf, I., Ismail, A.L., Lawan, M.A., Ali, U.A and Nasir, S. (2021).
Reliability modelling and analysis of client–server system using
Gumbel–Hougaard family copula. Life Cycle Reliability and Safety
Engineering. DOI 10.1007/s41872-020-00159-4
⎯ Yusuf, I., Ismail, A. L., Singh, V. V., Ali, U. A. and Sufi, N. A. (2020).
‘Performance Analysis of Multi‑computer System Consisting of Three
Subsystems in Series Configuration Using Copula Repair Policy’. SN
Computer Science 1:241