Sensitivity Weaknesses in Application of some Statistical Distribution in First Order Reliability Methods

It has been observed and shown that in some examples a sensitivity analysis of the first order reliability index results in increasing reliability index, when the standard deviation for a stochastic variable is increased while the expected value is fixed. This unfortunate behaviour can occur when a stochastic variable is modelled by an asymmetrical density function. For lognormally, Gumbel and Weibull distributed stochastic variables it is shown for which combinations of the/3-point, the expected value and standard deviation the weakness can occur. In relation to practical application the behaviour is probably rather infrequent. A simple example is shown as illustration and to exemplify that for second order reliability methods and for exact calculations of the probability of failure this behaviour is much more infrequent.