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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     author = {A. L. Kurakin and L. I. Lobkovsky},
     title = {Mathematical model of flaw detection},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {99--111},
     publisher = {mathdoc},
     volume = {27},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_6_a6/}
}
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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/