Traditionally

it is assumed that microgrids transition seamlessly from grid-connected operation to islanded mode in the event of sudden main grid outages. In reality

the islanding process

especially unintentional islanding

is rarely seamless. Instead

it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch

variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process

we propose a stochastic microgrid scheduling model that incorporates chance-constrained resilience measures. Specifically

the resilience measure is defined as the probability of successful islanding (PSI)

that is

the probability that a microgrid can mitigate the generation-demand imbalance caused by the disconnection of the PCC switch

variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices

which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude

the proposed PSI-based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed-integer linear programming (MILP) formulation. Case study results validate the proposed method

showing that the PSI estimation error is reduced to less than 8%

compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular

the necessity of accounting for DER tripping in the PSI calculation was demonstrated.