Search for Author, Title, Keyword
Optimization of maintenance costs of a pipeline for a V-shaped hazard rate of malfunction intensities
More details
Hide details
Systems Research Institute, Polish Academy of Sciences ul. Newelska 6, 01-447 Warszawa, Poland and The John Paul II Catholic University of Lublin, ul. Konstantynów 1 H, 20-708 Lublin, Poland
Publication date: 2018-03-31
Eksploatacja i Niezawodność – Maintenance and Reliability 2018;20(1):46-56
In this paper I focus on an evaluation of maintenance costs of a water distribution system (WDS), if a concept of a value of money in time is taken into account. Contrary to more classical approaches, instead of a constant yield, a strictly stochastic process (i.e., the one-factor Vasicek model) of an interest rate is assumed. Such an assumption presents uncertain, future behaviour of the yield in a more correct, realistic way. Moments of failures of connections in a WDS are generated using the Monte Carlo simulations via a new kind of a convex hazard rate function (HRF), which is proposed in this paper. Moreover, quality of a pipeline and a number of previous failures have direct influence on statistical properties of this introduced HRF. Apart from an analysis of the simulated output (like the maintenance costs), the Kiefer-Wolfowitz method is used for a better adjustment of one of parameters of a WDS – deterministic and unconditional replacement (i.e., planned replacement) time of each pipe. Algorithms, for both the simulations of the failure moments for the introduced HRF and the optimization step, are also provided. Additionally, some examples of a WDS for a crisp and a fuzzified settings are statistically analysed
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.
Broadie M, Cicek D, Zeevi A. General bounds and finite-time improvement for the Kiefer-Wolfowitz stochastic approximation algorithm. Operations Research 2011; 59(5): 1211–1224,
Buckley J J. Simulating Fuzzy Systems. Berlin Heidelberg: Springer-Verlag, 2005,
Clark R M, Thurnau R C. Evaluating the risk of water distribution system failure: A shared frailty model. Front. Earth Sci. 2011; 5(4):400–405.
Fadaee M J, Tabatabaei R. Estimation of failure probability in water pipes network using statistical model. Engineering Failure Analysis 2011; 18: 1184–1192,
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.
Glasserman P. Monte Carlo Methods in Financial Engineering. New York: Springer, 2004.
Gonzalez A, Pons O, Vila M A. Dealing with uncertainty and imprecision by means of fuzzy numbers. International Journal of Approximate Reasoning 1999; 21: 233–256,
Homem-de-Mello T, Bayraksan G. Monte Carlo sampling-based methods for stochastic optimization. Surveys in Operations Research and Management Science 2014; 19: 56–85,
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,
Kanakoudis V K, Tolikas D K. Assessing the performance level of a water system. Water, Air, and Soil Pollution 2004; 4: 307–318,
Kleiner Y, Adams B J, Rogers J S. Long-term planning methodology for water distribution system rehabilitation. Water Resources Research. August 1998; 34(8): 2039–2051,
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,
Lee K H. First Course on Fuzzy Theory and Applications. Berlin Heidelberg: Springer, 2005.
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.
Malinowski J. A newly developed method for computing reliability measures in a water supply network. Operations Research and Decisions 2016; 26(4): 49–64.
Marchionni V, Cabrala M, Amadoa C, Covasa D. Water supply infrastructure cost modelling. Procedia Engineering 2015; 119: 168–173,
Neelakantan T R, Suribabu C R, Lingireddy S. Optimisation procedure for pipe-sizing with break-repair and replacement economics. Water SA. April 2008; 34(2): 217–224.
Nguyen H T. A Note on the Extension Principle for Fuzzy Sets. Journal Mathematical Analysis and Applications 1978; 64: 369–380,
Nowak P, Romaniuk M. Application of Levy processes and Esscher transformed martingale measures for option pricing in fuzzy framework. Journal of Computational and Applied Mathematics 2014; 263: 129–151,
Nowak P, Romaniuk M. Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making. Soft Computing 2017; 21(10): 2575–2597,
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,
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.
Rokstad M M, Ugarelli R M. Minimising the total cost of renewal and risk of water infrastructure assets by grouping renewal interventions. Reliability Engineering and System Safety 2015; 142: 148–160,
Romaniuk M. Application of Markov chain and interest rate process for forecasting of costs of maintenance of pipelines. In: Wittmann J, Wieland R. (eds.) Simulation in Umwelt- und Geowissenschaften. Workshop Müncheberg 2015. Aachen: Shaker Verlag, 2015.
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,
Romaniuk M, Nowak P. Monte Carlo methods: theory, algorithms and applications to selected financial problems. Warszawa: ICS PAS, 2015.
Røstum J. Statistical modelling of pipe failures in water networks. Ph.D. dissertation. 2000.
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,
Interval-based, nonparametric approach for resampling of fuzzy numbers
Maciej Romaniuk, Olgierd Hryniewicz
Soft Computing
Stochastic Models, Statistics and Their Applications
Maciej Romaniuk
Predictive Maintenance Scheduling with Failure Rate Described by Truncated Normal Distribution
Iwona Paprocka, Wojciech Kempa, Grzegorz Ćwikła
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
Intelligent Systems in Production Engineering and Maintenance
Edward Kozłowski, Dariusz Mazurkiewicz, Beata Kowalska, Dariusz Kowalski
Research on high-pressure hose with repairing fitting and influence on energy parameter of the hydraulic drive
Mykola Karpenko, Olegas Prentkovskis, Šarūnas Šukevičius
Eksploatacja i Niezawodnosc - Maintenance and Reliability
Information Processing and Management of Uncertainty in Knowledge-Based Systems
Maciej Romaniuk
Discrete and Smoothed Resampling Methods for Interval-Valued Fuzzy Numbers
Maciej Romaniuk, Olgierd Hryniewicz
IEEE Transactions on Fuzzy Systems
Estimation of maintenance costs of a pipeline for a U-shaped hazard rate function in the imprecise setting
Maciej Romaniuk, Olgierd Hryniewicz
Eksploatacja i Niezawodność – Maintenance and Reliability
Selected problems of ambiguity of the dual price of water in the post-optimization analysis of the water supply system
Jacek Wawrzosek, Szymon Ignaciuk, Andrzej Bochniak
Eksploatacja i Niezawodność – Maintenance and Reliability
Research on pipe burst in water distribution systems: knowledge structure and emerging trends
Chenwan Wang, Qiang Xu, Zhimin Qiang, Yan Zhou
Journal of Water Supply: Research and Technology-Aqua
Journals System - logo
Scroll to top