I'm not sure many consulting engineers use reliability directly in their daily work. Most of the reliability work is done at the universities and testing labs where lab tests of structural elements are studied in terms of their variability. Also, the actual tested strength is studied as to how sensitive the strength is to variations in parameters that go into estimating the strength.
For instance, a concrete beam's flexural strength is affected by flange width, B; web width b; depth to reinforcing, d; concrete strength, f'c; reinforcing yield, fy, etc. Each of these has larger and smaller direct effects on strength....f'c not affecting the flexural strength as much as d does. So each parameter has a level of influence on predicted strength, and each parameter has a degree of variability in the field vs. estimated. (i.e. - d can be strictly calculated but in the field, it varies based on how accurate were the chairs, did they sit tight to the forms, were the forms cut/sized correctly, etc.)
One of the most prolific writers on reliability in structural engineerins is a professor named Bruce Ellingwood. Don't know where he currently works but an internet search could bring him up.
On paper I wrote some time ago for a graduate class dealt with taking a large number of tests of composite metal deck/concrete slabs and developing a phi factor (strength reduction factor) for the shear bond mode of failure. Again, lots of variables in the predictive equation for shear that had different amounts of influence on the shear strength (the weight of the variable) and different amounts of variability. These combined into a sort of statistical weighted average to develop a probability of failure for various phi factors (0.65, 0.75, 0.85) and these in turn were compared to other probabilities of failure of shear mode failures (i.e. concrete beam shear failure).
So the reliability that I'm aware of is focused on studying the statistical character of an estimate of strength and ends up being eventually published in a code somewhere.