Mathematical model of flaw detection

Abstract

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.