Mathematical model of flaw detection
- 30 Downloads
Analyzing the efficiency of preventive measures based on probability relations of reliability theory demonstrates that these measures principally rank below nondestructive testing (defectoscopy, or flaw detection), which represents a direct diagnostic method for preventing failures and accidents. The proposed mathematical model rests on the interpretation of nondestructive testing as observations of the current state of the basic reliability parameter, namely, the failure rate. Analytical relations of the model are obtained using Kolmogorov’s equations for the limiting probabilities of the state graph of an item–defectoscope system. The model has the following parameters: the failure and restoration rates of an item, the probabilities of errors of the first and second kind of the faults' detection, and the frequency of item testing. The results demonstrate the technological and economic efficiency of flaw detection. Here, the frequency of testing is more important for economic efficiency than small probabilities of errors. The model can be used to optimize performance specifications for the design of flaw detection equipment. The numerical examples approximately correspond to conditions of offshore industry.
Keywordsdetection of defects of constructions reliability accidents gamma-percentile life failure and restoration rates Kolmogorov’s equation for state graph errors of the first and second kind economic efficiency earning/spending rates
Unable to display preview. Download preview PDF.
- 1.W. Feller, An Introduction to Probability Theory and Its Applications, 3rd ed. (Wiley, New York, Chichester, Brisbane, Toronto, 1970), Vols. 1, 2.Google Scholar
- 2.GOST (State Standard) No. 27.002-89: The Reliability of the Technique. Basic Concepts. Terms and Definitions.Google Scholar
- 3.A. M. Polovko and S. V. Gurov, Principles of Reliability Theory (BKhV-Peterburg, St. Petersburg, 2006) [in Russian].Google Scholar
- 5.N. P. Aleshin and V. G. Shcherbinskii, Radiation, Ultrasonic and Magnetic Particle Inspection of Fabricated Metal Products (Vyssh. Shkola, Moscow, 1991) [in Russian].Google Scholar
- 6.Ultrasonic Control, Ed. by V. A. Troitskii (Inst. Elektrosvarki im. E. O. Patona NAN Ukrainy, Kiev, 2006) [in Russian].Google Scholar
- 7.N. A. Rimskii-Korsakov and V. A. Sychev, “Trends in developments and applications of hydroacoustic media for detection, identification, research, and monitoring of underwater objects,” in Proceedings of the 9th ScientificPractical Conference on Forecasting of Emergencies, May 14–15, 2009 (Ministerstvo Chrezvych. Situatsii, Moscow, 2009), pp. 188–202.Google Scholar
- 8.E. L. Lehman, Testing Statistical Hypotheses (Wiley, Chapman Hall, New York, London, 1959).Google Scholar
- 9.A. L. Kurakin, “Bayes approach to hypotheses testing in monitoring problems,” General Intern. Services (F&B, New York, 2011), ID: 10230867. http://www.lulu.com/Google Scholar
- 10.A. L. Kurakin, “Algorithm for object detecting during continuous monitoring,” SOFTWARE & SYSTEMS, No. 3, 166–169 (2011).Google Scholar