In this paper we propose a new family of cumulative indexes for measuring scientific performance which can be applied to many metrics, including h index and its variants (here we apply it to the h index, h(2) index and Google Scholar's i10 index). These indexes follow the general principle of repeating the index calculation for the same publication set. Using bibliometric data and reviewer scores for accepted and rejected fellowship applicants we examine how valid the cumulative variant is compared to the original variant. These analyses showed that the cumulative indexes result in higher correlations with the reviewer scores than their original variants. Thus, the cumulative indexes better reflect the assessments by peers than the original variants and are useful extensions of the original indexes. In contrast to many other measures of scientific performance proposed up to now, the cumulative indexes seem not only to be effective, but they are also easy to understand and calculate.