In order to incorporate the scheme proposed in the Methodology section, the following steps are taken:
The sub-criteria that can act as random numbers or have an uncertain nature must be recognized. Among the considered factors, sub-criteria related to hydrologic features such as hurricane flood elevation, and sub-criteria that could have an effect on flood risk such as ‘percent of not at risk equipment (the percentage of equipment that is not at risk of flooding, for example, due to a high elevation or being water proofed)’ are considered as factors with an uncertain nature. Table 4 shows the complete list of the identified uncertain factors.
The probability distribution functions for each sub-criterion's permissible values are obtained. This is done by examining different distributions such as normal, log normal, and Weibull, and then determining the best distribution function to fit to observed values of each sub-criterion for the 14 WWTPs. In Table 4, distribution functions and the corresponding parameters fitted to different sub-criteria are also presented.
Based on the fitted distribution functions, 100 random values are generated for selected sub-criteria, and the resiliency values for 14 WWTPs are recalculated. The data generation yields 100 resiliency values for each WWTP.
Fitted distributions to the sub-criteria with an uncertain nature
| Sub-criteria . | Distribution . |
|---|---|
| Ra1 (Hurricane flood elevation) | Nakagamid (aa = 7.248 bb = 119.79) |
| Ro1 (Additional load in time of flooding) | Generalized extreme value (a = 0.30095 b = 52.524 cc = 82.361) |
| Ro2 (Critical flood elevation) | Weibull (a = 10.821 b = 15.377) |
| Ro3 (Maximum inundation depth) | Generalized extreme value (a = −0.75455 b = 2.091 c = 4.7072) |
| Ro4 (Percent of not at risk equipment) | Lognormal (a = 0.21304 b = −0.333) |
| Ro5 (DMR violations) | Generalized Pareto (a = −1.4076 b = 3.6558 c = −0.39702) |
| Rs3 (Total risk avoided) | Generalized Pareto (a = −0.18964 b = 13.557 c = −0.96838) |
| Sub-criteria . | Distribution . |
|---|---|
| Ra1 (Hurricane flood elevation) | Nakagamid (aa = 7.248 bb = 119.79) |
| Ro1 (Additional load in time of flooding) | Generalized extreme value (a = 0.30095 b = 52.524 cc = 82.361) |
| Ro2 (Critical flood elevation) | Weibull (a = 10.821 b = 15.377) |
| Ro3 (Maximum inundation depth) | Generalized extreme value (a = −0.75455 b = 2.091 c = 4.7072) |
| Ro4 (Percent of not at risk equipment) | Lognormal (a = 0.21304 b = −0.333) |
| Ro5 (DMR violations) | Generalized Pareto (a = −1.4076 b = 3.6558 c = −0.39702) |
| Rs3 (Total risk avoided) | Generalized Pareto (a = −0.18964 b = 13.557 c = −0.96838) |
aShape.
bScale.
cLocation.
dNakagami is a distribution similar to gamma distribution.