On simulation of maintenance costs for water distribution system with fuzzy parameters

Abstract

Article citation info: (*) Tekst artykułu w polskiej wersji językowej dostępny w elektronicznym wydaniu kwartalnika na stronie www.ein.org.pl IntroductionThe main aim of each water distribution system (WDS, water pipes network) is to deliver water of desirable quality and assumed quantity for customers. In order to meet these requirements, maintenance services, like repairs and replacements of broken or malfunctioned parts, are required.The literature devoted to the problems of simulation of the WDS behaviour and to analysis of its reliability is very rich (see, e.g, [3, 4, 7, 10, 11, 15, 17, 19, 25, 29] for a description of various approaches, and [16,28] for a more detailed review of methods and literature). Because of a necessary long-time horizon planning (e.g. 20 or even 50 years), an influence of a value of the money in the future on maintenance costs should be taken into account. Also such a problem is addressed in many papers.For example, in [20], the main aim is to estimate and validate various cost functions for different types of assets of a WDS, if their hydraulic (e.g., flow, pump head, pump power) and physical characteristics (e.g., volume, material, nominal diameter) are stored in a specially prepared data base. A method of a linear regression is used to model a dependency between various types of the costs (like an equipment cost) and the mentioned characteristics of a pipe (like a nominal diameter) based on data from several Portuguese urban water utilities. However, a method for a calculation of a present value of the total costs is not developed there in a more detailed way.Contrary to the previous paper, in [12], let's say, a "macro-management" approach for a WDS rehabilitation problem with a real long-time horizon is widely discussed. In this paper, both an economics and hydraulic capacity of a WDS is analysed, if a deterioration of a pipe follows the Hazen-Williams equation. The total costs are related RomAniuk m. on simulation of maintenance costs for water distribution system with fuzzy parameters. Eksploatacja i niezawodnoscmaintenance and Reliability 2016; 18 (4): 514-527, http://dx.doi.org/10.17531/ein.2016.4.6. to a rehabilitation of a pipe and some additional maintenance costs (mainly breakage repair costs). To model the breakage rate, the exponential dependency on an age of a pipe is assumed. The present value of the total costs is then calculated using a constant discount rate. The main aim of the whole procedure is to minimize the total costs associated with a rehabilitation, if some hydraulic constraints, necessary for a quality and a quantity of the supplied water, are preserved. As mentioned in this paper, an analysis period for such a procedure is typically equal to 30-60 years.There are also more specialized approaches to the problem of the costs estimation. For example, in [25], an optimisation procedure for a problem of minimising the costs is also described. In this case, the authors express the total cost of a renewal, risk and an unavailability of a WDS as one func...

Optimization of maintenance costs of a pipeline for a V-shaped hazard rate of malfunction intensities

“…Such a simplification is possible (see, e.g., [29] for a more detailed discussion), but usually the relevant period is modelled by some random variable (like the exponential distribution, see, e.g., [11]). In the following, I also assume, that a time, which is necessary for a repair or a replacement, is given by some random distribution.This paper can be seen as a further development of some ideas, which were previously discussed in [25,26], but it is also a proposition of completely new ones. Hence, my current contribution is fourfold.…”

“…Moreover, sometimes it can not be appropriately modelled, if only a probabilistic approach is used. Therefore, I further develop an idea, which was discussed in [26], and some parameters of the assumed models are described by fuzzy numbers. It means, that they are not completely precise (i.e., "crisp") but they are, in some way, imprecise ("near to / about") and can be given as experts' opinions (even in a form of linguistic variables).…”

“…And a fuzzy setting is widely used in an analysis of possible financial decisions (see, e.g., [20,21]). Fourthly, in contrary to [25,26], a more sophisticated model of time intervals of transitions between the states of a pipeline is proposed now. The intervals between the malfunctions are generated using the introduced HRF, and the times of repairs and replacements can be drawn from various probabilistic distributions.…”

“…I distinguish two types of these costs (separately for a repair and a replacement) with two parts for each of them -a constant part (which is independent of length of time of a service) and a variable part (which depends on a random value of time of a repair or a replacement). Therefore, the considered model is closer to practical situations.It should be pointed out, that the stochastic model of the interest rate (i.e., the one factor-Vasicek model, which is assumed in this paper) is directly embedded into the Monte Carlo simulations, as in [26]. To the best knowledge of the author, such an approach is still a new idea, which is not even considered in other papers.…”

An integrated econometric model for bus replacement and determination of reserve fleet size based on predictive maintenance

“…Other tools may contribute to the development of a new model for the optimization of bus replacement, such as Fuzzy Logic and Support Vector Machine (SVM) [14,17,18,41,44,48,53]. For predictive maintenance, specifically using oil analysis, several mathematical models are appropriate [2,12,13,22,46].…”