Geodesic
Mathematical model of flaw detection
Matematičeskoe modelirovanie, Tome 27 (2015) no. 6, pp. 99-111.

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Analysis of prophylactic measures based on the theory of reliability shows that all such measures principally inferior to the nondestructive testing (defectoscopy, or flaw detection), being a direct diagnostic method preventing failures and accidents. The offered mathematical model is based on the interpretation of nondestructive testing as observations of the real state of current reliability parameter. The model is derived from a graph, which states include tested object and testing (detecting) system conditions. Analytical relationships are deduced from Kolmogorov's equations for the limiting probabilities of the states. Model parameters are: intensities of failures and restorations, probabilities of errors and the period of testing. The frequency of testing turns to be more important than equipment quality. Optimization is possible from technological or from economic points of view. Results may be used for optimization of technical specifications for the system of defects detection. Numerical examples approximately correspond to the conditions of oil and gas extrction on the shelf.
Keywords: constructions defects detection reliability, gamma-percent resource, rate of failures and recoveries, Kolmogorov’s equation for graph of states, errors of the 1-st and the 2-nd kinds, economical effectiveness, earning/spending rate.
Mots-clés : accidents 
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A. L. Kurakin; L. I. Lobkovsky. Mathematical model of flaw detection. Matematičeskoe modelirovanie, Tome 27 (2015) no. 6, pp. 99-111. http://geodesic.mathdoc.fr/item/MM_2015_27_6_a6/

[1] W. Feller, An Introduction to Probability Theory and Its Applications, v. 1, 2, Third Edition, John Willey Sons, New York–Chichester–Brisbane–Toronto, 1970 | MR

[2] Nadezhnost v tekhnike. Osnovnye poniatia. Terminy i opredelenia, GOST 27.002-89

[3] A. M. Polovko, S. V. Gurov, Osnovy teorii nadezhnosti, BKhV-Peterburg, S-Petersburg, 2006, 704 pp.

[4] A. L. Kurakin, “Prognostication of data-bases safety”, Software System, 1998, no. 2, 13–17 (In Russian)

[5] N. P. Aleshin, V. G. Shcherbinskii, Radiotsionnaia, ultrazvukovaia i magnitnaia defektoskopiia metalloizdelii, Vysshaia Shkola, M., 1991, 271 pp.

[6] V. A. Troitskii (ed.), Ultrazvukovoi control, Instsitut elektrosvarki im. E. O. Patona NAN Ukrainy, Kiev, 2006, 220 pp.

[7] N. A. Rimsky-Korsakov, V. A. Sychev, “Trends in developments and applications of hydroacoustic media for detection, identification, research, and monitoring of underwater objects”, The IXth Sci-Practical Conf. “Forecasting of emergencies” (14–15 May 2009, Moscow), RF Ministry of emergency situations, 2009, 188–202 (In Russian)

[8] E. L. Lehman, Testing Statistical Hypotheses, John Willey Sons Inc., New York; Chapman Hall, Limited, London, 1959 | MR | MR | Zbl

[9] A. L. Kurakin, Baiesovskii podkhod k proverke gipotez v zadachakh monitoringa, General International Services, F, Inc., New York, 2011, 26 pp.

[10] A. L. Kurakin, “Algoritm obnaruzheniia obektov v usloviiakh nepreryvnogo monitoringa”, Software System, 1998, no. 2, 13–17 (In Russian)