scholarly journals Mathematical modelling of dynamic characteristics of repair process for system operating under maintenance contracts

2021 ◽  
Author(s):  
Nataša Kontrec ◽  
Jelena Vujaković ◽  
Marina Tošić ◽  
Stefan Panić ◽  
Biljana Panić
Keyword(s):  
Differential Equation ◽  
Repair Process ◽  
Mathematical Form ◽  
Repair Rate ◽  
Integral Characteristics ◽  
Optimal Values ◽  
Time Required ◽  
Probability Density Function Pdf ◽  
System Operating ◽  
Evaluation Of System Performance

Repair rate is very important parameter in a system maintainability and it can be defined as frequency of the successfully performed repair actions on failed component per unit of time. This paper analyses the integral characteristics of a stochastic repair rate for corresponding values of availability in the system operating under maintenance contracts. The equation for the envelope line of the probability density function (PDF) maximums of the repair rate has been provided. This new expression can be used for planning of base stock levels and capacities of repair facilities. Namely, in that way instead of repair rate PDF equation, for some calculations we can use envelope line parameters, which are expressed in simpler mathematical form, to reduce the time required for calculations and prediction and enhance reactions in failure events. For analytical and numerical evaluation of system performance, the annual repair rate PDFs are analyzed like particular solutions of corresponding differential equation, while the existence of singular solution is considered and analyzed under different conditions. Moreover, we have derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.

scholarly journals Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2360
Author(s):  
Nataša Kontrec ◽  
Jelena Vujaković ◽  
Marina Tošić ◽  
Stefan Panić ◽  
Biljana Panić
Keyword(s):  
Differential Equation ◽  
Repair Process ◽  
Mean Value ◽  
Mathematical Form ◽  
Repair Rate ◽  
Integral Characteristics ◽  
Optimal Values ◽  
Time Required ◽  
Probability Density Function Pdf ◽  
System Operating

The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.

Płyty kołowe Hencky’ego–Bolle’a spoczywające na podłożu sprężystym Własowa

2020 ◽  
Vol 29 (4) ◽  
pp. 444-453
Author(s):  
Mykola Nagirniak
Keyword(s):  
Differential Equation ◽  
Circular Plate ◽  
Significant Influence ◽  
Single Layer ◽  
Medium Thickness ◽  
Cross Sectional ◽  
Equation Solution ◽  
Integral Characteristics ◽  
Two Parameter ◽  
Plate Deflection

The work presents the equations of the theory of symmetrical plates, resting on one-way, single-layer, two-parameter Vlasov’s subsoil. Two cases of differential equation solution of the plate deflection of thin and medium thickness on the ground substrate were analyzed depending on the size of the integral characteristics UÖD and 6ÖD. The example of loading the circular plate with a Pk load evenly distributed over the edge was considered and shows dimensionless graphs of deflection, bending torques and transverse forces in the plate and in the ground subsoil. The effect of the Poisson’s coefficient of the plate on deflection values and cross-sectional forces was investigated. The Poisson’s number has been shown to have a significant influence on deflection values and bending torque, however shown negligible effect on transverse forces values.

The Automatic-Control System as a Communication Channel

1968 ◽  
Vol 1 (7) ◽  
pp. 251-254
Author(s):  
D. A. Bell
Keyword(s):  
Differential Equation ◽  
Nineteenth Century ◽  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Mathematical Theory ◽  
Communication Channel ◽  
Electric Signal ◽  
Mathematical Form

The science of communication was pursued in mathematical form much earlier than the science of control, since the former can be traced back at least to the mid nineteenth century when Kelvin solved the differential equation of the propagation of an electric signal along a cable of negligible inductance; and in the first quarter of the nineteenth century a number of well-known applied mathematicians (for example, Heaviside, Carson, Sobel, Nyquist) were associated with telecommunications. Moreover, Shannon's elaboration and consolidation of the mathematical theory of communication came before the major developments in automatic control. It is therefore profitable to examine whether any of the theorems or techniques which have been developed in connection with telecommunications can be applied to problems in automatic control.

scholarly journals Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Lina Yang ◽  
Yuan Yan Tang ◽  
Xiang Chu Feng ◽  
Lu Sun
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Transformation Model ◽  
Geometric Transformation ◽  
Mathematical Form ◽  
Partial Differential ◽  
Distorted Image

Geometric (or shape) distortion may occur in the data acquisition phase in information systems, and it can be characterized by geometric transformation model. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation to remove the distortion for the geometric restoration. Consequently, finding a mathematical form to approximate the distorted image plays a key role in the restoration. A harmonic transformation cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the geometric restoration. In this paper, a novel wavelet-based method is presented, which consists of three phases. In phase 1, the partial differential equation is converted into boundary integral equation and representation by an indirect method. In phase 2, the boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. In phase 3, the plane integral equation and representation are then solved by a method we call wavelet collocation. The performance of our method is evaluated by numerical experiments.

P-70: Improving Defect Repair Rate in Automatic Repair Process of Color Filter Manufacturing

2018 ◽  
Vol 49 (1) ◽  
pp. 1452-1455
Author(s):  
Li Peng ◽  
Liu Tingting ◽  
Feng Meng ◽  
Li Jian ◽  
Li Pingfu ◽  
...  
Keyword(s):  
Repair Process ◽  
Color Filter ◽  
Repair Rate ◽  
Defect Repair

Soft computing for availability optimization of a crushing system of sugar plant using PSO

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anil Kr. Aggarwal ◽  
Amit Kumar
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Pso Algorithm ◽  
Repair Rate ◽  
System Availability ◽  
Content Type ◽  
First Order ◽  
Availability Analysis ◽  
Sugar Plant ◽  
Optimal Values

PurposeIn this paper, the objective is to perform mathematical modeling to optimize the steady-state availability of a multi-state repairable crushing system of a sugar plant using the evolutionary algorithm of Particle Swarm Optimization (PSO). The system availability is optimized by evaluating the optimal values of failure and repair rate parameters concerned with the subsystem of the system.Design/methodology/approachMathematical modeling of the multi-state repairable system is performed to develop the first-order differential equations based on the exponential distribution of the failure and repair rates. These differential equations are recursively solved to obtain the availability under normalizing conditions. The availability of the system is optimized by using the PSO algorithm. The results obtained by PSO are validated by using the Genetic Algorithm (GA).FindingsThe availability analysis of the system concludes that the cane preparation (F1) is critical of the crushing system and the optimized availability of the system using PSO is achieved as high as 87.12%.Originality/valueA crushing system of the sugar plant is evaluated as it is the main system of the sugar plant. The maintenance data associated with failure and repair rate parameters were analyzed with the help of maintenance records/logbook and by conducting personal meetings with maintenance executives of the plant. The results obtained in the paper helped them to plan maintenance strategies accordingly to get optimal system availability.

The Absorption and Diffusion of Water in Rubber

1937 ◽  
Vol 10 (4) ◽  
pp. 660-672
Author(s):  
H. A. Daynes
Keyword(s):  
Differential Equation ◽  
Water Vapor ◽  
Diffusion Theory ◽  
Gas Diffusion ◽  
Dominant Factor ◽  
Rubber Sheet ◽  
Linear Dimensions ◽  
Desorption Time ◽  
Time Required ◽  
And Diffusion

Abstract A new differential equation of diffusion is put forward to represent the movements of water vapor through rubber in accordance with the osmotic theory of absorption. Experiments are described which, together with the evidence quoted from existing knowledge, confirm a number of predictions as to differences between the absorption of a gas and of water vapor by rubber. These predictions deal with the shapes of the absorption- and desorption-time curves between narrow and wide limits of humidity, the relative times required for absorption and desorption, and the variation of absorption and desorption periods with thickness of the rubber sheet. The results are definitely inconsistent with the simple gas-diffusion theory, which is often assumed to apply to water in rubber. It is established that the shape of the humidity-absorption curve is a dominant factor in determining time-water content relations. Except for changes over very restricted ranges of humidity, the absorption- and desorption-time curves are of different shape, and desorption is much more rapid than absorption. The periods required for absorption and desorption are greater, the higher the humidity and the higher the hygroscopicity of the rubber. The law that the time required to reach a given stage of saturation varies as the square of the linear dimensions of the sample (the shape being constant) is equally true for diffusion, according to the old and new equations.

scholarly journals Convergence Analysis from the Solution of Riccati’s Fractional Differential Equation by Using Polynomial Least Squares Method

2020 ◽  
Vol 21 (1) ◽  
pp. 7-14
Author(s):  
Dian Nuryani ◽  
Endang Rusyaman ◽  
Betty Subartini
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Numerical Approach ◽  
Percentage Error ◽  
Mathematical Form ◽  
Fractional Differential

Riccati's Fractional Differential Equation (RFDE) has become a topic of study for researchers because RFDE can model variety of phenomenon in science such as random processes, optimal control and diffusion problems. Phenomena that can be modeled in a mathematical form can make it easier for humans to analyze several things from that phenomenon. RFDE generally does not have an exact solution, therefore a numerical approach solution is needed, one of the methods that gives good accuracy to the actual or exact solution is Polynomial Least Squares, where the errors calculated based on mean absolute percentage error (MAPE) produce a percentage below 1%. In addition, the convergence of a sequence from approximate solutions indicates that the sequence will converge to a solution.

scholarly journals Stochastic and Percolating Models of Blocking Computer Networks Dynamics during Distribution of Epidemics of Evolutionary Computer Viruses

2019 ◽  
Vol 7 (3) ◽  
pp. 7-27 ◽  
Author(s):  
S. A. Lesko ◽  
A. S. Alyoshkin ◽  
V. V. Filatov
Keyword(s):  
Differential Equation ◽  
Percolation Threshold ◽  
Computer Networks ◽  
Structural Information ◽  
Blocking Probability ◽  
Complex Model ◽  
Time Interval ◽  
Virus Propagation ◽  
Information Characteristics ◽  
Time Required

The paper presents a complex model of the dynamics of virus epidemies propagation in computer networks, based on topological properties of computer networks and mechanisms of the viruses spread. On one hand, this model is based on the use of percolation theory methods, which makes it possible to determine such structural-information characteristics of networks as the dependence of the percolation threshold on the average number of connections per one node (network density). On the other hand, the dynamic processes of stochastic propagation in computer networks of evolving viruses are observed when anti-virus programs become outdated and postponed. The paper discusses the concept of percolation threshold, provides an equation for the dependence of the percolation threshold of a network on its density obtained by analyzing numerical simulation data. The dynamics of virus epidemies were studied through two approaches. The first one is based on the description of transition diagrams between states of nodes, after which a system of kinetic differential equations for the virus epidemies is constructed. The second is based on considering the probabilities of transitions between possible states of the entire network. A second-order differential equation is obtained in this article, and a boundary value problem is formulated. Its solution describes the dependence of the network blocking probability on the blocking probability of an individual node. The solution also makes it possible to estimate the time required to reach the percolation threshold. The model incorporates the evolutionary properties of viruses: previously immunized or disinfected nodes can be infected again after a certain time interval. Besides, the model incorporates a lag of the anti-virus protection. Analysis of the solutions obtained for the models created shows the possibility of various modes of virus propagation. Moreover, with some sets of values of differential equation coefficients, an oscillating and almost periodic nature of virus epidemies is observed, which largely coincides with real observations.

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