ABSTRACT
Generally calculation of probability PB employs probability of failure as a measure and require a knowledge of the joint distribution of all random value parameters. It is Level-3. Probability of non failure can be written in terms of safety margin :f(R − S) == R − S ≥ 0, is PB = P(> 0). As an alternative to PB, a reliability index is often defined as βB =−1(PB) =−−1(PF), where PF = 1 − PB = ∫FfX(x)dx is failure probability and F is the failure set. β is interpreted as minimum distance between central point and limit state surface (Figure 1). In general this integral cannot be computed analytically. Method solving this integral is rather difficult because of its complexity. There are many based on simplification and additional assumptions (Madsen, 1986). Sometimes we can simplifying problem to the basis variables which are jointly normally distributed
we can use form PF =(−βC) quantity βC is second order moment reliability index for safety problem. In another words we can use methods of Level-2 or even Level-1 to evaluated index of reliability. The limit condition = 0 implicate reliability index β≤m/µd and m = (Rm − Sm)/((µ2R +µ2S)1/2) where R and S with index m denotes mean value of R and S, µ denotes standard deviation. Simplifying = R − S to one dimension space margin of safety area is shown on Figure 1 where S = Sd − Sk, R = Rd − Rk.
