Catchment basins are used to protect residential areas and highways from mud slides. A mudslide basin has a capacity of C, which is a random variable with a COV of 0.2. The expected 25-year maximum inflow is denoted F with a COV of 1.0. Develop an expression for computing the reliability index and the failure probability assuming lognormal probability distributions for both C and F.

Compute the reliability index and the failure probability assuming that the mean ratio of C/F is 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, and 3.0. What mean ratio would you recommend to protect a highway section with average traffic volume of 5000 vehicles per day at an average speed of 50 mph?

Discuss and justify your selection.