This paper considers the problem of function estimating for times to failure translation from one mode to another. This problem arises, for example, when there is data on failures of products in vitro tests and you need to estimate the reliability of the same type products with actual test conditions. For simplicity, we consider the case where MTBF have linear relation. The proposed method is based on minimizing the Kolmogorov-Smirnov statistic, which is used to test the homogeneity of two progressively censored samples. A special feature of the proposed statisticis using the Kaplan-Meier estimates of the reliability function for each sample. Provided conjecture homogeneity of two samples, the distribution of statistics does not depend on the type of distribution of failures. This paper proposes a method for calculating the exact distributions of these statistics. Tables of exact distributions probabilities are presented for a wide range of possible values of the volumes of samples. By means of statistical modeling a table of acceleration factor values is calculated and its histograms are presented.
Keywords: non-parametric statistics, the Kolmogorov-Smirnov test, Kaplan-Meier estimate, progressive censoring.
Timonin V., Tyannikova N. Progressively censored sample comparison - numerical methods for homogeneity statistic distributions and study of communication parameters estimating by Monte Carlo method. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 89-100
The article describes the method for calculating the stability of a rod under simultaneous action of axial force and torque, considering changing the torsion of the rod when it’s bent. The method is based on the use of the complete system of equations. The following cases are considered: end clamped rod, rod with a hinged support, the rod in the form of compressed and twisted console. Diagrams of dependence of the critical axial force versus the critical torque are obtained, i.e., the range of rod stability for the case of loading is determined.
Dubrovin V., Butina T. Modeling the stability of compressed and twisted rods in precise problem statement. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 3-16
Within the framework of solving the problem of active control of the elastic and damping elements of multi-wheeled vehicle (MWV) suspension brackets investigating the properties of suspension bracket families designed both for different travels and for different loading is of great importance. Their kinematic schemes can be also rather various. It is not feasible to collect the required amount of information for families of vehicles of different design and operating characteristics. Performing a full analytical study to determine the appropriate characteristics is not possible. This problem could be successfully solved only by simulation. A mathematical model of the MWV motion is developed. The characteristic feature of the model is that the vehicle speed is not set forcedly, but it is generated by the interaction of the rotating wheeled propellers with the supporting base. It results in high accuracy in modeling real processes of MWV moving along an uneven road. The developed model can be applied to research various laws of multi-wheeled vehicle suspension bracket control.
Zhileykin M., Sarach E. Mathematical model of movement of the multi-wheeled vehicles with torsional flexible bearing system. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 17-40
The article describes an analytical solution to the model problem about stratified flow wave action on the underwater pipeline in the case of the circulation flow. Numerical computations of the hydrodynamic reactions for the real sea conditions are performed. The values of the flow parameters at which the wave-making drag and the lift capacity of the pipeline reaches its maximum are determined.
Vladimirov I., Korchagin N., Savin A. Hydrodynamic reactions in the model of circulatory streamlining the pipeline by bottom sea currents. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 41-57
The article considers the problem of determining the pressure on the body surface streamlined by a gas flow with a small supersonic speed (M < 1,5).The economic algorithm for calculating the pressure on the part of the surface of blunt bodies of revolution is developed. Examples of flow calculations over spheres and ellipsoids with different semi-axes ratios are presented. Comparison with accurate numerical calculations shows the effectiveness of the proposed approach.
Kotenev V., Sysenko V. Calculation of the pressure when streamlining blunt bodies with small supersonic speeds. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 58-67
The article considers the problems of coolant flow computational diagnostics in a closed circulation loop. The mathematical models of acoustic waves in two-phase flow are developed. Indirect diagnostic information, contained in the flow vibrational spectra recorded by regular systems is used. The inverse eigenvalue problem is formulated. Solving it the optimization approach is implemented. It is supposed that partial criteria are presented by continuous, Lipschitz, not everywhere differentiable, multi-extremal functions. Search of global solutions was performed using a new hybrid algorithms integrating stochastic algorithm of variable space viewing and deterministic methods of local search. A numerical example of model diagnosing the phase composition of the coolant in the circulation loop of nuclear reactor plant is presented.
Sulimov V., Shkapov P. Hybrid methods of computer diagnosis of two-phase flow in the circulation loop. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 68-88
A model for calculation of a rock stress-strain state considering creep is suggested. The algorithm for finite element solving the three-dimensional creep problem using finite-difference scheme of Euler's method with respect to time is presented. The specialized software is developed allowing the computer to build 3D-models of rock areas based on the initial series of 2D images, obtained with the seismic data, and to perform finite element calculation of variations in rock strain-stress state with time. Numerical simulation of rock stress-strain state was conducted on the example of a zone of the Astrakhan oil and gas field. It was found that there occurs rock mass rising in some points, and in the other points it can slope down with time. The creep rate of different layers is not the same — the highest values of the creep rate are realized in the layers of clay and sand, filled with fluid, which have the most notable creep properties. The developed algorithm and software for numerical simulation proved to be quite effective and can be applied to the study of rock stress-strain state.
Dimitrienko Y., Yurin Y. Finite element simulation of the rock stress-strain state under creep. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 101-118