What sort of metrics have you used or seen to measure the resiliency (not reliability) of the electric grid?

Resiliency seems to have a particularly squishy definition, or lack thereof, and means many things to many people. I believe it means how well the grid recovers after an upset (e.g., generator suddenly going offline, an attack from Russia, etc.). As such, any metrics would have to be established for a given circumstance, and to systematically establish such metrics would require compiling a list of historical and potential upsets, conducting an FMEA to analyze the effects of such upsets, and then list the fixes. Then, the metrics on the fixes could be compiled based on real world data after a few years of analyses.

In various areas of the utility, each view the perspective of resiliency different having worked in generation, customer facing, as well as T&D. It is true utilities base most of the metrics on interruptions more as a reliability aspect as it is easier to measure. When I was in Operations' Analysis, we did look at the system holistically as a risk analysis to determine a long-term planning/prioritization approach. Considerations included the number of times alternative generation or networks had to engage; number of planned and unplanned outages/interruptions; costs of replacements/repairs; number of OT hours, age of the equipment, diminishing labor pools of specialty areas such as splicing for a downtown network, changes in RICE reducing  customers having diesel generators as backup to their critical functions resulting in more dependency on the utility, etc. Resiliency is a work used a lot as an adjective to sell grid changes without many standard industry metrics.

What I like to use when discussing resiliency and reliability with upper managers (industrial, commercial and institutional energy users) are two metrics: unplanned power interruptions (reliability)  in hours/year and frequency of power interruptions (resiliency) in times per year which these unplanned power interruptions happened.

Combining these two metrics you get a pretty good picture of the "grid strength". I used it very successfully for example when one of my clients (a 6 MW demand packaging industrial company) was complaining about the number of hours per year and the frequency of the occurrences. 

I suggested a higher voltage connection (they were connected at 13 kV back then) - namely 138 kV by means of installing a 138 kV line connecting the plant to a close by 138 kV line owned by the local utility company and building a 10 MVA 138 kV/13.8 kV substation.

The client loved the idea of reaching a better reliability and resiliency - roughly speaking the unplanned interruptions at the close by 138 kV circuit (as I checked at the regulator's website) was 1/10 of the 13.8 kV and the frequency of the interruptions also 1/10! 

Bottom line: the client accepted the proposed concept of a higher voltage connection, which then demand less than 2 USD Million, was inaugurated in just 6 months (above picture) and savings were reached in two "fronts" - wire fees were of course a lot lower and the reduction of interruptions of power significantly reduced their revenue losses.

I have not seen any specific references to accepted metrics for resiliency.  There are recommendations on how to be more resilient such as  preparedness, mitigation measures, response capabilities, and recovery mechanisms.  However, these are not metrics.  For reliability, we have mean time between failure as a metric for a piece of equipment.  We have availability (as opposed to reliability) as a metric for equipment being available to operate, whether iti is operating or not.  It would seem to me that recovery is the key to resilience.  Perhaps, mean time to recover could be a metric for a system.  One thing I would say is that the government often has conflicting requirements.  A mid-West water supplier has emergency diesel engines available to continue to pump water in the event of a power outage due to a storm.  When a storm is forecast, the engines are turned on so as to be ready for such an emergency.  However, as the engines are designated as emergency engines, they are limited in the number of hours that they can operate outside of an emergency.  If the storm in question does not produce a power outage, the hours of operation count against that limit.  Clearly, the system is more resilient when the engines are running in anticipation of a power outage (preparedness, mitigation measures, and response capabilities).  And the system recovery will be aided by having these engines in operation.  Nevertheless, the EPA is adamant that such operation does not constitute an emergency and continues to count those operating hours against the operating limit.