RESEARCH PAPER
Estimation of maintenance costs of a pipeline for a U-shaped hazard rate function in the imprecise setting
| 1 | Systems Research Institute Polish Academy of Sciences ul. Newelska 6, 01-447 Warszawa, Poland Warsaw School of Information Technology, ul. Newelska 6, 01-447 Warsaw, Poland |
| 2 | Systems Research Institute Polish Academy of Sciences ul. Newelska 6, 01-447 Warszawa, Poland |
Publication date: 2020-06-30
Eksploatacja i Niezawodność – Maintenance and Reliability 2020;22(2):352–362
KEYWORDS
water distribution systemmaintenance costsconvex hazard rate functionMonte Carlo simulationsfuzzy setsshadowed sets
ABSTRACT
In this paper, we discuss imprecise settings for an evaluation of the maintenance costs of a water distribution system (WDS). Moments of failures of pipes are modelled using a newly proposed three-piece convex hazard rate function (HRF) for which number
of previous failures is taken into account, too. Both fuzzy sets and shadowed sets are used to model the impreciseness of important
parameters of this HRF and the costs of maintenance services. Contrary to more classical and widely-used approaches to cost
analysis (i.e. a constant yield or nominal value of money), a strictly stochastic process (i.e. the one-factor Vasicek model) of an
interest rate is assumed in the analysis of maintenance costs. This approach models future behaviour of the interest rate (i.e. the
future value of money) in a more realistic way. Respective algorithms together with exemplary results of numerical simulations for
two setups, which are related to fuzzy and shadowed sets, are also provided.
REFERENCES (30)
1.
Amani N, Ali N M, Mohammed A H, Samat R A. Maintenance and management of wastewater system components using the condition index system, prediction process and costs estimation. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2013; 15(2): 161-168.
2.
Blokus A, Kołowrocki K. Reliability and maintenance strategy for systems with aging-dependent components. Quality and Reliability Engineering International 2019, https://doi.org/10.1002/qre.25....
3.
Dąbrowska E, Soszyńska-Budny J. Monte Carlo Simulation Forecasting of Maritime Ferry Safety and Resilience, 2018 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), Bangkok 2018, 376-380, https://doi.org/10.1109/IEEM.2....
4.
Fadaee M J, Tabatabaei R. Estimation of failure probability in water pipes network using statistical model. Engineering Failure Analysis 2011; 18: 1184-1192, https://doi.org/10.1016/j.engf....
5.
Farmani R, Kakoudakis K, Behzadian K, Butler D. Pipe Failure Prediction in Water Distribution Systems Considering Static and Dynamic Factors. Procedia Engineering 2017, 186: 117-126, https://doi.org/10.1016/j.proe....
6.
Folkman S. Water Main Break Rates In the USA and Canada: A Comprehensive Study. Utah State University 2018.
7.
Gil M A, Hryniewicz O. Statistics with Imprecise Data. In: Meyers R A (ed.). Encyclopedia of Complexity and Systems Science. New York: Springer-Verlag, 2009.
8.
Glasserman P. Monte Carlo Methods in Financial Engineering. New York: Springer, 2004, https://doi.org/10.1007/978-0-....
9.
Grzegorzewski P. Trapezoidal approximation of fuzzy numbers based on sample data. In: Hüllermeier E, Kruse R, Hoffmann F (eds.). Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. Springer Berlin Heidelberg 2010: 402-411, https://doi.org/10.1007/978-3-....
10.
Grzegorzewski P. Fuzzy number approximation via shadowed sets. Information Sciences 2013; 225: 35-46, https://doi.org/10.1016/j.ins.....
11.
Hryniewicz O, Kaczmarek K, Nowak P. Bayes statistical decisions with random fuzzy data - An application for the Weibull distribution. Eksploatacja i Niezawodnosc - Maintenance and Reliability. 2015; 17(4): 610-616. https://doi.org/10.17531/ein.2....
12.
Kleiner Y, Adams B J, Rogers J S. Long-term planning methodology for water distribution system rehabilitation. Water Resources Research 1998; 34(8): 2039-2051, https://doi.org/10.1029/98WR00....
13.
Kumar G, Jain V, Gandhi O P. Steady-state availability analysis of repairable mechanical systems with opportunistic maintenance by using semi-Markov process. Int J Syst Assur Eng Manag. 2014; 5(4): 664-678, https://doi.org/10.1007/s13198....
14.
Lee K H. First Course on Fuzzy Theory and Applications. Berlin Heidelberg: Springer, 2005.
15.
Lubiano M A, Salas A, Carleos C, de la Rosa de Sáa S, Gil M Á. Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data. International Journal of Approximate Reasoning 2017; 88: 128-147, https://doi.org/10.1016/j.ijar....
16.
Liu Z, Kleiner Y, Rajani B, Wang L, Condit W. Condition Assessment Technologies for Water Transmission and Distribution Systems. Washington DC: U.S. Environmental Protection Agency, 2012; EPA/600/R-12/017.
17.
Malinowski J. A newly developed method for computing reliability measures in a water supply network. Operations Research and Decisions 2016; 26(4): 49-64.
18.
Marchionni V, Cabrala M, Amadoa C, Covasa D. Water supply infrastructure cost modelling. Procedia Engineering 2015; 119: 168-173, https://doi.org/10.1016/j.proe....
19.
Neelakantan T R, Suribabu C R, Lingireddy S. Optimisation procedure for pipe-sizing with break-repair and replacement economics. Water SAl 2008; 34(2): 217-224, https://doi.org/10.4314/wsa.v3....
20.
Nguyen H T. A Note on the Extension Principle for Fuzzy Sets. Journal Mathematical Analysis and Applications 1978; 64: 369-380, https://doi.org/10.1016/0022-2....
21.
Pedrycz W. Shadowed Sets: Representing and Processing Fuzzy Sets. IEEE Transactions on Systems, Man and Cybernetics- Part B 1998; 28(1): 103-109, https://doi.org/10.1109/3477.6....
22.
Pietrucha-Urbanik K, Studziński A. Case study of failure simulation of pipelines conducted in chosen water supply system. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2017; 19 (3): 317-322, https://doi.org/10.17531/ein.2....
23.
Rojek I, Studziński J. Comparison of different types of neuronal nets for failures location within water-supply networks. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2014; 16 (1): 42-47.
24.
Rojek I, Studziński J. Detection and localization of water leaks in water nets supported by an ICT system with artificial intelligence methods as away forward for smart cities. Sustainability 2019; 11(2), https://doi.org/10.3390/su1102....
25.
Romaniuk M. On simulation of maintenance costs for water distribution system with fuzzy parameters. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2016; 18(4): 514-527, https://doi.org/10.17531/ein.2....
26.
Romaniuk M. Optimization of maintenance costs of a pipeline for a V-shaped hazard rate of malfunction intensities. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2018; 20(1): 46-54, https://doi.org/10.17531/ein.2....
27.
Romaniuk M, Hryniewicz O. Discrete and smoothed resampling methods for interval-valued fuzzy numbers. IEEE Transactions on Fuzzy Systems 2020, https://doi.org/10.1109/TFUZZ.....
28.
Romaniuk M, Nowak P. Monte Carlo methods: theory, algorithms and applications to selected financial problems. Warszawa: ICS PAS, 2015.
29.
Røstum J. Statistical modelling of pipe failures in water networks. Ph.D. dissertation. 2000.
30.
Scheidegger A, Leitão J P, Scholten L. Statistical failure models for water distribution pipes - A review from a unified perspective. Water Research 2015; 83: 237-247, https://doi.org/10.1016/j.watr....
CITATIONS (3):
1.
Information Processing and Management of Uncertainty in Knowledge-Based Systems
Maciej Romaniuk
Maciej Romaniuk
2.
A novel interpretable model of bathtub hazard rate based on system hierarchy
Yi-Mu Du, C.P. Sun
Reliability Engineering & System Safety
Yi-Mu Du, C.P. Sun
Reliability Engineering & System Safety
3.
A study of the Inverse Gaussian Process with hazard rate functions-based
drifts applied to degradation modelling
Luis Rodríguez-Picón, Luis Méndez-González, Iván Pérez-Olguín, Jesús Hernández-Hernández
Eksploatacja i Niezawodnosc - Maintenance and Reliability
Luis Rodríguez-Picón, Luis Méndez-González, Iván Pérez-Olguín, Jesús Hernández-Hernández
Eksploatacja i Niezawodnosc - Maintenance and Reliability
RELATED ARTICLE
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.