Error Amplification in Failure Probability Estimates of Small Errors in Response Surface Approximations

Response surface methods which approximate the actual performance function using simple algebraic equations are widely used in structural reliability studies. The response surface approximations are often used to estimate the reliability of a structure. Errors in the response surface approximation affect the results of reliability analysis. This work investigates the error in the failure probability estimated using a response surface approximation. It is observed that small errors in the response surface may amplify to large errors in the failure probability. It is observed that the amplification occurs when the failure surface is far away from the response mean and the DOE has more points near the mean. Another situation is when the failure region is a small island encompassed within the safe region, and the points in the DOE fail to capture the failure region. Analytical and engineering application examples are investigated to understand the amplification of error in the failure probability.