The ideal way of eliminating errors in a large scale software system is to test the software with all possible inputs, providing sufficiently large amount of execution time. However, in practice, the test must be performed within given budget and time limits. Therefore, to perform the test under given constraints, we have to properly select inputs and determine the execution time for each selected inputs. This paper studies the distribution of number of errors at a given time as well as the distribution of time required to reduce the number of errors to a certain level. We assumed that error occurrence times are distributed exponentially (not necessarily identical) and the number of errors at the initial stage is known or estimable.