A problem in high integrity systems is that the failure rate of software is low and therefore difficult to measure. We have adapted importance sampling to enable the measurement of software and system reliability for high integrity systems. In essence, it is the equivalent of elevated temperature life testing for hardware components. The technique utilizes the operational profile and expected exception conditions to create both a testing program and the definition of importance factors. These allow testing results to be evaluated quantitatively in order to conservatively estimate failure rates lower than 1 per million hours. Measurement of extremely low failure rate software is important because there is still no quantitative evidence that any software development methodology will consistently deliver systems that will achieve a specified level of safety or reliability.