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Fault-tolerance in commercial aircraft applications is typically achieved by redundancy. In such redundant systems the primary component is checked before the start of a flight to see if it operates correctly. The aircraft will not take off unless the primary is functioning. Airplane manufacturers must certify the airplane systems to be safe for flight. One means of safety certification is by safety analysis which shows that the probability of failure in a typical flight is bounded. The probability bound requirement for a system is based on the criticality of system failure. Usually backup components are checked at intervals that span multiple flights. The first backup may be checked more frequently than the second or higher levels. This leads to flights where the system may have latent faults in the backup components. The probability of failure in such cases varies from flight to flight due to the different exposure times for components in the system.