The weakly hard real-time model is an abstraction for applications, including control systems, that can tolerate occasional deadline misses, but can also be compromised if a sufficiently high number of late terminations occur in a given time window. The weakly hard model allows us to constrain the maximum number of acceptable missed deadlines in any set of consecutive task executions. A big challenge for weakly hard systems is to provide a schedulability analysis that applies to a general task model, while avoiding excessive pessimism. In this work, we develop a general weakly hard analysis based on a Mixed Integer Linear Programming (MILP) formulation. The analysis applies to constrained-deadline periodic real-time systems scheduled with fixed priority and no knowledge of the task activation offsets, while allowing for activation jitter. Our analysis considers two common policies for handling missed deadlines, i.e., (i) letting the job continue until completion or (ii) killing its execution immediately. For this policy, ours is the first and only m-k analysis currently available. Experiments conducted on randomly generated task sets show the applicability and accuracy of the proposed technique as well as the improvements with respect to competing techniques.