Application of Efficient Methods for Inspection Sensitivity

Nondestructive evaluation (NDE) inspections play a vital role in the reliability of structural components. NDE inspections are simulated using a probability-of-detection curve (POD) that is obtained experimentally. In this paper a methodology using the expectation operator was developed to obtain the sensitivity of the probability-of-failure (POF) with respect to parameters of the POD via Monte Carlo Sampling (MCS). The methodology scales to any number of inspections and can be integrated with existing MCS methods. Sensitivities of the probability-of-failure with respect to the parameters of a POD curve were calculated for several numerical examples then compared against analytical and numerical finite difference solutions. Nomenclature crack size probability distribution before inspection crack size probability distribution after nth inspection probability-of-detection curve complementary POD, equal to one minus POD X crack size random variable parameter of POD curve scaling parameter such that the integral of equals one probability of detecting a crack probability of not detecting a crack probability of failure after nth inspection probability of failure sensitivity with respect to after nth inspection expected value operator with respect to number of samples generated from. number of samples detected by the nth inspection process and removed number of samples not detected by the nth inspection process I