Transformed conditional probabilities in the analysis of stochastic sequences

The need to use unsophisticated probability-based approaches and models in the structural safety analysis of the structures subjected to annual extreme service, snow and wind actions is discussed. Statistical parameters of single and coincident two extreme variable actions and their effects are analysed. Monotone and decreasing random sequences of safety margins of not deteriorating and deteriorating members are treated, respectively, as ordinary and generalized geometric distributions representing highly-correlated series systems. An analytical analysis of the failure or survival probabilities of members and their systems is based on the concepts of transformed conditional probabilities of safety margin sequences whose statistically dependent cuts coincide with extreme loading situations of structures. The probability-based design of members exposed to coincident extreme actions is illustrated by a numerical example.