The likelihood of hitting the target and the conditional probability of kill given a hit are the most important parameters in determining of the gunfire probability of kill against a target. The geometric and step function models are the most common models for calculating the probability of kill given a hit. In the geometric model, each hit to target is treated independently and the number of hits required to achieve a target kill is a random variable whereas in the step function model, the most likely kill occurs only once a fixed number of hits have been achieved. Although in many of situations that the mean number of hits-to-kill is the same for each model, these models can produce significant differences in the prediction effectiveness. Thus the main aim of this paper is to introduce a new modeling approach with a more general distribution for the number of hits-to-kill. It is referred to this new proposed model as the discrete Weibull model. This model has several desirable properties for example itis configurable to various classes of damage mechanism and it includes geometric and step function models with suitable parameter selection. We use it to explore the influence of various damage accumulation models on the predicted effectiveness of weapon-target engagements.