Smart grids provide services at the basis of a number of application sectors, several of which are critical from the perspective of human life, environment or financials. It is therefore paramount to be assisted by technologies able to analyze the smart grid behavior in critical scenarios, e.g. where cyber malfunctions or grid disruptions occur. In this paper, we present a stochastic modelling framework to quantitatively assess representative indicators of the resilience and quality of service of the distribution grid, in presence of accidental faults and malicious attacks. The results from the performed analysis can be exploited to understand the dynamics of failures and to identify potential system vulnerabilities, against which appropriate countermeasures should be developed. The features of the proposed analysis framework are discussed, pointing out the strong non-linearity of the involved physics, the developed solutions to deal with control actions and the definition of indicators under analysis. A case study based on a real-world network is also presented.