Conditional expectations in the evaluation of fault-tolerant systems

The concept of conditional expectations for comparing fault-tolerant designs is introduced. Specifically, the traditional mean time to failure (MTTF) is shown to be one case of a more general conditional expectation function, E{T_f|t_l⩽T _f⩽t₂}, defined as the expected time of failure T_f, given that t_l⩽T_f⩽t₂ for time t. Two examples are considered in detail to provide an illustration of the use and importance of conditional expectations