Optimal times for software release when repair is imperfect

The determination of the optimal release time for a new piece of software is of primary importance in the process of software development. We study a model where initially there are N faults in the software each with failure detection rate [lambda](t), but where the probability of a perfect repair of a fault when found is p (in general repair is not perfect). We investigate various cost models for this situation and give some insight into how the optimal release times and costs for the software vary with p and [lambda](t).