Appendix C 3
(i) The element is checked operative at the beginning of a certain flight. Then
(ii)The state of the item is unknown at the beginning of a certain flight. Then where Pprior (Failure) is the probability that the failure of the element has occurred prior to a certain flight.
(5) If there is only an effect when failures occur in a certain order, the calculation should account for the conditional probability that the failures occur in the sequence necessary to produce a Failure Condition.
c. Calculation of the “Average Probability Per Flight” of a Failure Condition: The next step is to calculate the "Average Probability Per Flight" for a Failure Condition, that is, the probability of a Failure Condition for each flight (which might be different, although all flights are "Average Flights") during the relevant time (for example, the least common multiple of the exposure times or the aircraft life) have to be calculated, summed up, and divided by the number of flights during that period. The principles of calculating are described below and are in more detail in ARP 4761.
Note: N is the quantity of all flights during the relevant time, and PFlight k is the probability that a Failure Condition occurs in flight k.
Example: In the special case of a duplex system (one component failure latent, the other detected), this method results in an "Average Probability Per Flight," which equals the product of both failure rates multiplied by the [ ]( ) ( ) P (Failure) P (Failure) P Failure t t , t exp d Flight Phase j j=1 n j 1 j j n i t t i=1 n i-1 i = = ∈ = − − ∑ ∑ ∫∏ − =1 1 l x x ( ) ( ) P (Failure) = P (Failure) P (Failure) exp d Flight prior prior i t t i=1 n i-1 i + − ⋅ − − ∫∏1 1 l x x ( ) ( ) P Failure Condition P Failure Condition k=1 NAverage per Flight Flight k N = ∑
Appendix C 4 "Average Flight" duration TF multiplied by one-half (50 percent) of the relevant exposure time.
d. Calculation of the “Average Probability Per Flight Hour” of a Failure Condition:
Once the "Average Probability Per Flight" has been calculated, it should be normalized by dividing it by the "Average Flight" duration TF in “Flight Hours” to obtain the "Average Probability Per Flight Hour." This quantitative value should be used in conjunction with the hazard category/effect established by the FHA to determine if it is compliant for the Failure Condition being analyzed.
( ) ( )P Failure Condition P Failure ConditionTAverage per FH Average per Flight F=