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An accurate prediction of the number of defects in a software product during system testing contributes not only to the management of the system testing process but also to the estimation of the product's required maintenance. Here, a new approach called ED3M is presented that computes an estimate of the total number of defects in an ongoing testing process. ED3M is based on estimation theory. Unlike many existing approaches the technique presented here does not depend on historical data from previous projects or any assumptions about the requirements and/or testers' productivity. It is a completely automated approach that relies only on the data collected during an ongoing testing process. This is a key advantage of the ED3M approach, as it makes it widely applicable in different testing environments. Here, the ED3M approach has been evaluated using five data sets from large industrial projects and two data sets from the literature. In addition, a performance analysis has been conducted using simulated data sets to explore its behavior using different models for the input data. The results are very promising; they indicate the ED3M approach provides accurate estimates with as fast or better convergence time in comparison to well-known alternative techniques, while only using defect data as the input.