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

Abstract

Article citation info: (*) Tekst artykułu w polskiej wersji językowej dostępny w elektronicznym wydaniu kwartalnika na stronie www.ein.org.pl IntroductionFrom the customers' point of view, the main aim of a water distribution system (which is further abbreviated as WDS) is to deliver water, moreover -water of desirable quality and in necessary quantity. Therefore, different maintenance services have to be performed, e.g., broken or simply malfunctioned pipes or other parts of a WDS should be repaired or replaced. Because water is an indispensable good for humans, therefore also scientific literature devoted to reliability of water distribution systems is abundant. Firstly, let us mention reviews of various methods, approaches and literature, which can be found in, e.g., [15,28,29]. The papers themselves are very varied -some of them concern hydraulic and physical characteristics of parts of a WDS (see, e.g., [4,17]), other discuss rather a "macro-management" of a WDS rehabilitation problem (see, e.g., [12,22]) or only a "micromanagement" scale (e.g., for a single building, see [1]). Even some monitoring systems for failures detection in a WDS are proposed (see, e.g., [23]).Usually, if maintenance costs for a WDS are considered, planning for a relatively long-time horizon should be taken into account. Such a time interval covers 20, 50 or even 60 years (see, e.g., [12]). Of course, one unit of money, which is paid now, and the same unit in 50-60 years, are not equal. Therefore, an influence of a future / present value of the money onto a calculation of the maintenance costs should be taken into account. However, most of the authors apply only a constant interest rate, as a discount factor, to calculate a present value of future cash flows. Such an assumption is, of course, too strong and unrealistic in practical situations. Therefore, in this paper I adopt a more realistic and complex model -a variable interest rate, which is described by the widely known one-factor Vasicek model. Moreover, some model for intensities of malfunctions of parts of a WDS has to be assumed. As it is proposed in literature, it can be based on selected physical aspects of a pipe and numerical equations (like the Hazen-Williams equation, see, e.g., [12]), it can be described with some type of Markov or semi-Markov process (see, e.g., [13,16,26]) or malfunctions are randomly generated using a hazard rate function (HRF). A 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): 46-56, http://dx.doi.org/10.17531/ein.2018.1.7. maciej RomAniuk OptimizatiOn Of maintenance cOsts Of a pipeline fOr a V-shaped hazard rate Of malfunctiOn intensitiesOptymalizacja kOsztów eksplOatacyjnych rurOciągu dla V-kształtnej funkcji intensywnOści uszkOdzeń* [29]. In this paper I propose a new kind of a HRF, which can be easily adapted to real-life data and which is very efficient during the Monte Carlo simulations. Very often in...

Selected problems of ambiguity of the dual price of water in the post-optimization analysis of the water supply system

“…Some models of problems with reliability or optimization of the cost and maintenance time of a water supply or sewage system are constructed on the statistical-stochastic basis [3,38]. Romaniuk [44][45][46] presents numerous numerical experiments focusing, for example, on optimizing the value of expected costs and duration of exploiting a water supply network, when the decision-making parameter is unconditional exchange time, i.e. when it is better to replace a network fragment instead of performing its another repair in the future.…”

Model of Predictive Maintenance of Machines and Equipment

“…We terminate the iteration when the sum of the variances can no longer be reduced or after performing a predetermined number of iterations. This method uses Equation (5) to determine the relationship between the X and Y variables by using an iterative algorithm. We constructed a Jacobi matrix, whose elements form partial derivatives of the approximation function (Equation (8)).…”

“…Quite a large number of maintenance optimization solutions, according to different criteria, exist in practice. Some modern solutions are listed in [1][2][3][4][5][6][7][8] and others. Most companies follow the maintenance program (maintenance regulations), which determines at what intervals and to what extent the equipment undergoes individual maintenance stages (inspection, preventive, predictive and proactive maintenance, revisions, diagnostic repairs, and overhauls, etc.).…”

Interval-based, nonparametric approach for resampling of fuzzy numbers

“…Its applications were described in numerous papers. For example, the authors of this paper used it to solve problems from such different areas as: pricing of financial and insurance instruments Romaniuk 2013, 2017), estimation of the maintenance costs of a water distribution system (Romaniuk 2016(Romaniuk , 2018 or Bayesian statistical decisions in reliability . The simulations which were considered in these papers, usually consisted in the generation of random hidden crisp origins, and respective membership functions (e.g., in the form of triangles with edges of random length).…”