We present a fast and exact algorzthm to compute maxzmum lzkelzhood estiniates for the number of faults anataally contazned in a software, uszng the hypergeometric software relaability model. The algorzthni is based on a rigorous matheinatical analysis of the growth behavzor of the lzkelzhood functzon for the model W e also clarify the stochastzc process underlying the model and prove a recursion formula whzch is central for most prevzous work on the hypergeometrzc software relzabzlzty model.