## 1 Introduction
There remains an ongoing debate within the research community regarding the necessity of a one-size-fits-all approach, given that resilience requirements can vary significantly depending on the specific context [19]. References [20; 21] propose resilience metrics based on the concept of a resilience trapezoid. Reference [22] utilizes metrics like outage duration and unserved energy demand to evaluate system resilience. Reference [23] assesses system performance under severe weather conditions using indicators such as the number of branches out of service, loss of load probability, and expected demand not supplied. In Reference [24], the authors quantify resilience in independent water-power networks based on the amount of power restored. Despite significant studies by academic researchers, the power system utilities are reluctant to invest in enhancing system resilience. There are no regulatory requirements or financial benefits to motivate such investments. This is mostly due to the rarity of extreme events and a lack of comprehension of the worth of resilience-driven investments. However, with the increasing frequency and severity of extreme weather events over the past decade, there is growing recognition among regulatory and planning bodies of the need to invest in measures that mitigate the overall societal costs resulting from such disruptions. The cost of these outages becomes even more significant when critical loads are considered. Itis, therefore, a prudent approach for the utilities to make resilience-driven investments, prioritizing the critical loads. Previous literature [25, 26, 27] has analyzed the investment strategies focusing on improving the performance of critical loads during extreme events. However, it is also important for the utilities to assess how this prioritization affects the performance of less critical loads and the overall system before committing to investments. This paper evaluates both infrastructural hardening and operational investment strategies to bolster the resilience of a system in regards to the performance of critical and non-critical load points. This paper contributes a valuable framework that can support the development of a value-based resilience model for long-term system planning. This work modifies and extends the distribution system resilience assessment framework presented in Reference [28] by incorporating the consideration of the critical loads, a method which is applicable to the evaluation of various resilience-driven investments. A key contribution of this paper is the development of a mathematical model that estimates system repair time, while accounting for load criticality. The sequence in which damaged components are repaired is influenced by the priority of the loads, the interdependence among the outage components, and the availability of repair crews. Since critical loads typically receive higher restoration priority, all available resources are initially assigned to these loads before being distributed to non-critical types. This necessitates a separate evaluation of the restoration of critical and non-critical loads during extreme events. This paper systematically models all possible scenarios arising from the prioritization of critical loads and varying crew availability while also factoring in component interdependencies and formulates a relationship to determine system repair time. Another significant contribution of this study is the introduction of new metrics designated as disconnected load point hours (DLH) and normalized DLH (NDLH) for evaluating distribution system resilience. Unlike conventional duration-based indices commonly used for resilience assessment, the DLH and NDLH metrics capture both the system's vulnerabilities and its ability to withstand extreme weather events. Moreover, the paper evaluates the efficacy of various investment strategies to improve system resilience, with a particular focus on the performance of critical loads.