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.

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.

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.

scholarly journals Phyllochron estimation in intercropped strawberry and monocrop systems in a protected environment

2012 ◽  
Vol 34 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Heloísa Ferro Constâncio Mendonça ◽  
Eunice Oliveira Calvete ◽  
Alexandre Augusto Nienow ◽  
Rosiani Castoldi da Costa ◽  
Lucas Zerbielli ◽  
...  
Keyword(s):  
Linear Regression ◽  
Production Systems ◽  
Block Design ◽  
Mean Value ◽  
Angular Coefficient ◽  
Degree Days ◽  
Camino Real ◽  
Fig Trees ◽  
Time Required ◽  
Strawberry Cultivars

The phyllochron is defined as the time required for the appearance of successive leaves on a plant; this characterises plant growth, development and adaptation to the environment. To check the growth and adaptation in cultivars of strawberry grown intercropped with fig trees, it was estimated the phyllochron in these production systems and in the monocrop. The experiment was conducted in greenhouses at the University of Passo Fundo (28º15'41'' S, 52º24'45'' W and 709 m) from June 8th to September 4th, 2009; this comprised the period of transplant until the 2nd flowering. The cultivars Aromas, Camino Real, Albion, Camarosa and Ventana, which seedlings were originated from the Agrícola LLahuen Nursery in Chile, as well as Festival, Camino Real and Earlibrite, originated from the Viansa S.A. Nursery in Argentina, were grown in white polyethylene bags filled with commercial substrate (Tecnomax®) and evaluated. The treatments were arranged in a randomised block design and four replicates were performed. A linear regression was realized between the leaf number (LN) in the main crown and the accumulated thermal time (ATT). The phyllochron (degree-day leaf-1) was estimated as the inverse of the angular coefficient of the linear regression. The data were submitted to ANOVA, and when significance was observed, the means were compared using the Tukey test (p < 0.05). The mean and standard deviation of phyllochrons of strawberry cultivars intercropped with fig trees varied from 149.35ºC day leaf-1 ± 31.29 in the Albion cultivar to 86.34ºC day leaf-1 ± 34.74 in the Ventana cultivar. Significant differences were observed among cultivars produced in a soilless environment with higher values recorded for Albion (199.96ºC day leaf-1 ± 29.7), which required more degree-days to produce a leaf, while cv. Ventana (85.76ºC day leaf-1 ± 11.51) exhibited a lower phyllochron mean value. Based on these results, Albion requires more degree-days to issue a leaf as compared to cv. Ventana. It was conclude that strawberry cultivars can be grown intercropped with fig trees (cv. Roxo de Valinhos).

scholarly journals Fractional Order Stochastic Differential Equation with Application in European Option Pricing

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Qing Li ◽  
Yanli Zhou ◽  
Xinquan Zhao ◽  
Xiangyu Ge
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Option Pricing ◽  
Memory Effect ◽  
Fractional Order ◽  
Mean Value ◽  
European Option ◽  
European Option Pricing ◽  
Proposed Model ◽  
Pricing Formula

Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.

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.

Helicopter Landing Ship: Undercarriage Strength and the Role of the Human Factor

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
E. Suhir
Keyword(s):  
Human Factor ◽  
Operation Time ◽  
Extreme Value Distribution ◽  
Mean Value ◽  
Helicopter Landing ◽  
The Times ◽  
The Moment ◽  
Normal Law ◽  
Time Required

We address, using probabilistic modeling and the extreme-value-distribution technique, the helicopter undercarriage strength in a helicopter-landing-ship situation. Our analysis contains an attempt to quantify, on the probabilistic basis, the role of the human factor in the situation in question. This factor is important from the standpoint of the operation time that affects the likelihood of safe landing during the lull period in the sea condition. The operation time includes (1) the time required for the officer-on-ship-board and the helicopter pilot to make their go-ahead decisions and (2) the time of actual landing. It is assumed, for the sake of simplicity, that both these times could be approximated by Rayleigh’s law, while the lull duration follows the normal law with a high enough ratio of the mean value to the standard deviation. Safe landing could be expected if the probability that it occurs during the lull time is sufficiently high. The probability that the helicopter undercarriage strength is not compromised can be evaluated as a product of the probability that landing indeed occurs during the lull time and the probability that the relative velocity of the helicopter undercarriage with respect to the ship’s deck at the moment of encounter does not exceed the allowable level. This level is supposed to be determined for the helicopter-landing-ground situation. The developed model can be used when developing specifications for the undercarriage strength, as well as guidelines for personnel training. Particularly, the model can be of help when establishing the times to be met by the two humans involved to make their go-ahead decisions for landing and to actually land the helicopter. Plenty of additional risk analyses (associated with the need to quantify various underlying uncertainties) and human psychology related efforts will be needed, of course, to make such guidelines practical.

Note on the Influence of the Heat Transfer Between the Surfaces as a Secondary Effect in Gas Lubrication

1969 ◽  
Vol 91 (1) ◽  
pp. 194-198
Author(s):  
V. N. Constantinescu
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Pressure Distribution ◽  
Mass Flow ◽  
Energy Equation ◽  
Load Capacity ◽  
Mean Value ◽  
Secondary Effect ◽  
Gas Lubrication ◽  
Isothermal Analysis

The problem of gas lubrication is examined by taking into account the energy equation and variation of viscosity with temperature. The velocity profiles and the pressure differential equation are deduced. When the temperatures T0, T1 of the two lubricated surfaces are constant, simple corrections can be obtained in order to estimate the influence of unequal temperatures of the two surfaces on pressure distribution, load capacity, and friction stresses in self-acting films and on pressure distribution and mass flow in externally pressurized bearings. However, as the influence of the transversal heat transfer manifests only through the intermediary of the variation of viscosity with temperature, the isothermal analysis can further on be used, provided that one takes a mean value for the viscosity, corresponding to a mean temperature Tm = (T0 + T1)/2.

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
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