EVALUATION MODEL OF THE RECOVERY PROCESSES OF NON-MARKOVIAN SYSTEMS, CONSIDERING THE ELEMENTS UNRELIABILITY UNDER ARBITRARY DISTRIBUTION LAWS
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Abstract
The subject of the study is the reliability of recoverable non–Markovian systems, functioning of which is described by arbitrary distribution laws. The purpose of the article is to develop a mathematical model of the functioning of modern computer systems under arbitrary laws of the distribution of stay duration in each of the states, taking into account the recovery system and the provision of spare elements. The main task is to develop an adequate model of the system functioning process, taking into account the non-Markovian character of the processes occurring in the system, its possible large dimension, and the presence of a hierarchical recovery system. Based on this model, a method for calculating the density of the system recovery time distribution has been developed. At the same time, a universal four-parameter distribution is proposed to describe random processes occurring in the system. Using this approximation, the calculation of the desired parameter of the recovery flow is performed by solving the Volterra integral equation with a difference kernel.
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Borisov, Yu.P. and Cvetnov, V.V. (1985), Matematicheskoe modelirovanie radiotehnicheskih sistem i ustroistv [Mathematical modeling of radio engineering systems and devices], Padio i svyaz, Moscow, 176 p.
Vilkomir, S.A. (1988), “Ob odnom metode rascheta nadezhnosti strukturno-slozhnih sistem s vosstanavlivaemimi elementami”, Nadezhnost i kontrol kachestva, No. 2, pp.23-26.
Barzilovich, E.Yu., Belyaev, Yu.K. and Kashtanov, V.A. (1983), Voprosi matematicheskoi teorii nadezhnosti [Questions of the mathematical theory of reliability], Radio i svyaz, Moscow, 376 p.
Demchenko, O.F., Davidov, V.B., Isaev, L.A., Ivanchihin, Yu.V., Makarenko B.I. and Raskin, L.G. (2000), Voprosi teorii ekspluatacii avtomatizirovannih transportnih sistem upravleniya [Questions of the theory of operation of automated transport control systems], HVU, Harkiv, 266 p.
Gnedenko, B.V., Belyaev, Yu.K. and Solovev, A.D. (1965), Matematicheskie metodi v teorii nadezhnosti [Mathematical Methods in Reliability Theory], Nauka, Moscow, 524 p.
Golovin, I.N., CHuvarigin, B.V. and SHura-Bura, A.E. (1984), Raschet i optimizaciya komplektov zapasnih elementov radioelektronnih system [Calculation and optimization of sets of spare elements of radio-electronic systems], Radio i svyaz, Moscow, 176 p.
Koks, D.R. and Smit, V.D. (1967), Teoriya vosstanovleniya [Recovery theory], Sov. Radio, Moscow, 299 p.
Nggada, S.H. (2012), “Software Failure Analysis at Architecture Level Using FMEA”, International Journal of Software, No. 6, pp. 61-74.
Obana, M. and Hanakawa, N. (2016), “Process Evaluation Based on Meeting Quality of Requirement Analysis Phase in Software Development Project”, Journal of Software Engineering and Applications, No. 7, pp. 828-843.
Ogheneovo, E.E. (2014), “Software Dysfunction: Why Do Software Fail?”, Journal of Computer and Communications, No. 2, pp. 25-35.
Pizzi, N.J. and Pedrycz W. (2008), “Effective Classification Using Feature Selection and Fuzzy Integration”, Fuzzy Sets and Systems, No. 21, pp. 2859-2872.
Pizzi, N.J. (2016), “Mapping Software Metrics to Module Complexity: A Pattern Classification Approach”, Journal of Software Engineering and Applications, No. 4, pp. 426-432.
Raja, U., Hale, J. E. and Hale, D. P. (2015), “Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects”, Journal of Software Engineering, No. 2, pp. 113-121.
Ushakov, I.A. (1991), Veroyatnostnie modeli nadezhnosti informacionno-vichislitelnih system [Probabilistic Models of Information and Computing Systems Reliability], Radio i svyaz, Moscow, 132 p.
Avizienis, A., Laprie, J.-C. and Randell B. (2001), “Fundamental Concepts of Dependability”, Research Report, No 1145, LAAS-CNRS, April,
Meeker, W.Q. and Escobar, L.A. (2016), Statistical Methods for Reliability Data, J.Wiley and Sons, New York, 704 p.
Bagdonavicius, V.B. and Nikulin, M.S. (2009), Accelerated Life Models: Modeling and Statistical Analysis, Chapman&Hall/CRC, Boca Raton, 360 p.
Antonov, A.V. and Nikulin, M.S. (2012), Statisticheskie modeli v teorii nadezhnosti [Statistical models in reliability theory], Abris, Moscow, 392 p.
Raskin, L.G. and Pustovoitov, P.E. (2002), “Reshenie mnogonomenklaturnih zadach upravleniya zapasami po veroyatnostnomu kriteriyu [Solving multi-item problems of inventory management by a probabilistic criterion]”, Vestnik NTU HPI, pp.49-53.