CONDITIONAL EXPECTATIONS IN THE EVALUATION OF FAULT-TOLERANT SYSTEMS

The Mean Time To Failure (MTTF) is a very common and useful measure for the evaluation and comparison of systems. It is well known, however, that the MTTF can be misleading when analyzing designs which include redundancy. This paper introduces the concept of conditional expectations for comparing fault-tolerant designs. Specifically, the traditional MTTF is shown to be one case of a more general conditional expectation function, E{T(f)\t1 less-than-or-equal-to T(f) less-than-or-equal-to t2}, defined as the expected time of failure, T(f), given that t1 less-than-or-equal-to T(f) less-than-or-equal-to t2. The conditional expectation can often provide significantly better insight into the overall quality of a particular design. Two examples are considered in detail to provide an illustration of the use and importance of conditional expectations.