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The technology of approximation of a convolution of a spline-weibull distribution

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Category: Information technologies, systems analysis and administration

Last Updated on 16 July 2014

Published on 21 March 2014

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Authors:

I.I. Shvatska, Oles Honchar Dnipropetrovsk National University, Assistant Lecturer of the Department of Mathematical Insurance EOM of Applied Mathematics Faculty, Dnipropetrovsk, Ukrainе.

O.H. Baibuz, Dr. Sci. (Tech.), Professor, Oles Honchar Dnipropetrovsk National University, Head of the Department of Mathematical Insurance EOM of Applied Mathematics Faculty, Dnipropetrovsk, Ukrainе.

Abstract:

Purpose. To develop the informational technology of statistical treatment of the data about mining and processing equipment failures using spline-distributions. To study the renewal model of the distribution function of spline-Weibull and to develop the algorithm of analytical approximation of convolution of spline-Weibull distributions in class of spline-exponential distributions, to evaluate the efficiency of the proposed approximation methods.

Methodology. We have used the modified method of maximum reality to reproduce the parameters of spline distributions. We have approximated the function of intensity of spline-Weibull distribution by pieces-constant functions of intensity of spline-exponential distribution with 1 and 3 knots. We have calculated the convolution of spline-exponential distributions by the method of characterizing functions.

Findings. The analysis of the approximation methods showed the necessity of usage of spline-Weibull distributions for analyzing the failures of mining and processing systems. We have proved that the approximation by spline-exponential distribution is universal as it lets us to conduct approximation procedures for any values of parameters of β_i, form, where i=1.2.

Originality. We have proposed the methods of construction of distribution function of convolution of spline-Weibull distribution, for which the exact analytical decision is impossible, and the approximation methods and algorithms of construction of the convolution of spline-exponential distributions with 1 and 3 knots.

Practical value. The new informational technology can be used for evaluation of the reliability and efficiency of complicated technical systems of the mining and processing industry in the conditions of accumulation of violations which require the usage of more adequate and reliable distributions based on Weibull distribution.

References:

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Pristavka, O.P. (1995), Splain-rozpodily u statystychnomu analizi [Spline Distributions in Statistical Analysis], Dnіpropetrovsk, Ukraine.

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Baibuz, O.H. and Pristavka, O.P. (2003), Splayny v nadezhnosti [Splines in Reliability], Dnіpropetrovsk, Ukraine

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