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.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