Appendix 3 Calculation of the average probability per flight hour

The purpose of this material is to provide guidance for calculating the ʽAverage Probability per Flight Hour’ for a failure condition so that it can be compared with the quantitative criteria of the AMC. The process of calculating the ʽAverage Probability per Flight Hour’ for a failure condition will be described as a four-step process and is based on the assumption that the life of an aeroplane is a sequence of ʽAverage Flights’. Step 1: Determination of the ʽAverage Flight’ Step 2: Calculation of the probability of a failure condition for a certain ʽAverage Flight’ Step 3: Calculation of the ʽAverage Probability per Flight’ of a failure condition Step 4: Calculation of the ʽAverage Probability Per Flight Hour’ of a failure condition a. Determination of the "Average Flight”. The "Average Probability per Flight Hour" is to be based on an "Average Flight". The average flight duration and average flight profile for the fleet of aeroplane to be certified should be estimated. The average flight duration should be estimated based on expectations and historical experience for similar types. The "Average Flight" duration should reflect the best estimate of the cumulative flight hours divided by the cumulative aeroplane flights for the service life of the aeroplane. The "Average Flight" profile should be based on the operating weight and performance expectations for the average aeroplane when flying a flight of average duration in an ICAO standard atmosphere. The duration of each flight phase (e.g. takeoff, climb, cruise, descent, approach and landing) in the "Average Flight" should be based on the average flight profile. Average taxi times for departure and arrival at an average airport should be considered where appropriate and added to the average flight time. The "Average Flight" duration and profile should be used as the basis for determining the "Average Probability per Flight Hour" for a quantitative safety assessment. b. Calculation of the Probability of a Failure Condition for a certain ʽAverage Flight’. The probability of a failure condition occurring on an ʽAverage Flight’ PFlight(failure condition) should be determined by structured methods (see Document referenced in paragraph 3.b(3) for example methods) and should consider all significant elements (e.g. combinations of failures and events) that contribute to the failure condition. The following should be considered:

(1)The component failure rates utilised in calculating the ʽAverage Probability per Flight Hour’ should be estimates of the mature constant failure rates after infant mortality and prior to wear-out. For components whose probability of failure may be associated with non-constant failure rates within the operational life of the aeroplane, a reliability analysis may be used to determine component replacement times (e.g. Weibull analysis). In either case, the failure rate should be based on all causes of failure (operational, environmental, etc.). If available, service history of same or similar components in the same or similar environment should be used. Ageing and wear of similarly constructed and similarly loaded redundant components, whose failure could lead directly, or in combination with one other failure, to a catastrophic or hazardous failure condition, should be assessed when determining scheduled maintenance tasks for such components. The replacement times, necessary to mitigate the risk due to ageing and wear of such components within the operational life of the aeroplane, should be assessed through the same methodology like other scheduled maintenance tasks that are required to comply with CS 25.1309 (refer to AMC 25-19 for guidance) and documented in the Airworthiness Limitations Section of the Instructions for Continued Airworthiness, as appropriate.

(2)If the failure is only relevant during certain flight phases, the calculation should be based on the probability of failure during the relevant ‘at risk’ time for the ‘Average Flight’.

(3)If one or more failed elements in the system can persist for multiple flights (latent, dormant, or hidden failures), the calculation should consider the relevant exposure times (e.g. time intervals between maintenance and operational checks/ inspections). In such cases the probability of the Failure Condition increases with the number of flights during the latency period.

(4)If the failure rate of one element varies during different flight phases, the calculation should consider the failure rate and related time increments in such a manner as to establish the probability of the failure condition occurring on an ʽAverage Flight’: It is assumed that the ʽAverage Flight’ can be divided into n phases (phase 1, ... , phase n). Let TF the ʽAverage Flight’ duration, Tj the duration of phase j and tj the transition point between Tj and Tj+1, j=1, ... ,n . I.e.

Let lj(t) the failure rate function during phase j, i.e. for t Î [tj-1,tj]. Remark: lj(t) may be equal 0 for all t Î [tj-1,tj] for a specific phase j. Let PFlight (Failure) the probability that the element fails during one certain flight (including nonflying time) and PPhase j (Failure) the probability that the element fails in phase j. Two cases are possible:

(i)The element is checked operative at the beginning of the certain flight. Then

(ii)The state of the item is unknown at the beginning of the certain flight. Then

where Pprior (Failure) is the probability that the failure of the element has occurred prior to the 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 the failure condition. c. Calculation of the Average Probability per Flight of a Failure Condition. The next step is to calculate the ʽAverage Probability per Flight’ for the failure condition, i.e. the probability of the failure condition for each flight (which might be different although all flights are ʽAverage Flights’) during the relevant time (e.g. the least common multiple of the exposure times or the aeroplane life) should be calculated, summed up and divided by the number of flights during that period. The principles of calculating are described below and also in more detail in the Document referenced in paragraph 3.b(3).

Where N is the quantity of all flights during the relevant time, and PFlightk is the probability that the Failure Condition occurs in flight k. 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 normalised 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 analysed.

[Amdt 25/14]

[Amdt 25/24] Amdt 25/27]