When a new computer software package is developed and all obvious erros removed, a testing procedure is often put into effect to eliminate the remaining errors in the package. One common procedure is to try the package on a set of randomly chosen problems. We suppose that whenever a program encounters an error, a system failure results. At this point the software is inspected to determine and remove the error responsible for the failure. This goes on for some time and two problems of interest are 1) to estimate the error rate of the software at a given time t, and 2) to develop a stopping rule for determining when to discontinue the testing and declare that the software is ready for use. In this paper, a model for the above is proposed as an estimation and stopping rule procedure.