Reliability Analysis Technique Using Local Approximation of a Cumulative Distribution Function

1. Abstract We propose a reliability analysis (RA) method that obtains the probability of failure by sequentially approximating the cumulative distribution function (CDF). This method uses the concept of the first order reliability method (FORM) in estimating the probability of failure but does not solve the optimization problem to obtain the most probable point (MPP). The goal of the proposed method is to obtain the probability when the limit state function value becomes a zero in the CDF. Usually, the CDF is not in explicit form, and thus we construct an approximate CDF using several points on the CDF and calculate the probability of failure using it. In order to build the approximate CDF, we employ two techniques. The first technique is an inverse MPP search for obtaining the limit state function value corresponding to a given probability. For enhancing efficiency and robustness, we improve the most probable point of inverse reliability (MPPIR) search method by modifying the function type checking criterion. The second is an approximate technique named as enhanced two-point diagonal quadratic approximation (ETDQA). The CDF is sequentially approximated by using ETDQA. Finally, various examples including convex, concave, and non-convex and non-concave functions are used to illustrate the effectiveness of the proposed RA method by comparing our results with those of other existing FORM based methods. 2.