New Index of Reliability

The index, β, is often used as a measure of second-moment reliability has several limitations. The new index, γ, avoids these limitations and has the same numerical value as β in elementary cases of second-moment reliability. γ is a function of the (generalized) Tchebysheff upper-bound to the probability of failure. γ is calculated for many different univariate, multivariate, and infinite-dimensional problems and, whenever possible, is compared with β. Cases are studied in which distribution characteristics other than the first two moments are known. These include knowledge of absolute moments, of moments of order higher than two, of positivity or unimodality, of the expectation of functions other than powers, of constraints on the maximum value of the probability density, of independence among the components of random vectors. γ is also used to make reliability comparisons between cases with the same value of β but with different safety regions.