AC 25.1309-1B Appendix F F.4 Calculation of the “Probability per Flight” of a Failure Condition over a period of N flights.
The next step is to calculate the probability per flight for the failure condition. In other words, the probability of the 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 airplane life) should be calculated, summed up, and divided by the number of flights during that period. The principles of calculating are described below and in more detail in SAE ARP 4761.
F.4.1.1 The element is checked operative at the beginning of the certain flight, Then:
∑𝑁𝑁𝑘𝑘=1 𝑃𝑃𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 𝑘𝑘 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑜𝑜𝑒𝑒𝑑𝑑𝑓𝑓𝑡𝑡𝑓𝑓𝑜𝑜𝑒𝑒 𝑓𝑓𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 𝑘𝑘)𝑃𝑃𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡(𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑜𝑜𝑒𝑒𝑑𝑑𝑓𝑓𝑡𝑡𝑓𝑓𝑜𝑜𝑒𝑒 𝑓𝑓𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) = 𝑁𝑁 F.4.1.2 The state of the single element is unknown at the beginning of the certain flight.
Then: ∑𝑁𝑁𝑘𝑘=1 𝑃𝑃𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 𝑘𝑘 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑜𝑜𝑒𝑒𝑑𝑑𝑓𝑓𝑡𝑡𝑓𝑓𝑜𝑜𝑒𝑒 𝑓𝑓𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 𝑘𝑘) 𝑓𝑓𝑖𝑖 𝑓𝑓𝑒𝑒𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡𝑜𝑜 𝑃𝑃𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑏𝑏𝑏𝑏 𝑓𝑓𝑒𝑒𝑑𝑑 𝑜𝑜𝑓𝑓 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) = 𝑃𝑃𝑝𝑝𝑝𝑝𝑓𝑓𝑝𝑝𝑝𝑝 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑓𝑓𝑓𝑓𝑜𝑜𝑓𝑓 𝑡𝑡𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) + 𝑃𝑃𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡(𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑓𝑓𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) 𝑛𝑛 𝑡𝑡𝑖𝑖 = 𝑃𝑃𝑝𝑝𝑝𝑝𝑓𝑓𝑝𝑝𝑝𝑝 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑓𝑓𝑓𝑓𝑜𝑜𝑓𝑓 𝑡𝑡𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) + �1 − 𝑃𝑃𝑝𝑝𝑝𝑝𝑓𝑓𝑝𝑝𝑝𝑝 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑓𝑓𝑓𝑓𝑜𝑜𝑓𝑓 𝑡𝑡𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡)� ∗ �1 − � 𝑓𝑓𝑒𝑒𝑒𝑒 �− � 𝜆𝜆 𝑓𝑓(𝑒𝑒)𝑑𝑑𝑒𝑒�� 𝑡𝑡𝑓𝑓=1 𝑖𝑖−1 Thus: 𝑃𝑃𝑝𝑝𝑎𝑎𝑝𝑝 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑜𝑜𝑒𝑒𝑑𝑑𝑓𝑓𝑡𝑡𝑓𝑓𝑜𝑜𝑒𝑒 𝑓𝑓𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) = 𝑃𝑃𝑝𝑝𝑝𝑝𝑓𝑓𝑝𝑝𝑝𝑝 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑓𝑓𝑓𝑓𝑜𝑜𝑓𝑓 𝑡𝑡𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡) + �1 − 𝑃𝑃𝑝𝑝𝑝𝑝𝑓𝑓𝑝𝑝𝑝𝑝 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑒𝑒𝑓𝑓𝑓𝑓𝑜𝑜𝑓𝑓 𝑡𝑡𝑜𝑜 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡)� ∗ �1 − ∏𝑛𝑛𝑓𝑓=1 𝑓𝑓𝑒𝑒𝑒𝑒 �− 𝑡𝑡∫ 𝑖𝑖 𝜆𝜆𝑓𝑓(𝑒𝑒)𝑑𝑑𝑒𝑒��𝑡𝑡𝑖𝑖−1 𝑁𝑁 Where N is the quantity of all flights during the relevant time, and Pflight k is the probability that the failure condition occurs in flight k.
F.5 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.
𝑃𝑃 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑜𝑜𝑒𝑒𝑑𝑑𝑓𝑓𝑡𝑡𝑓𝑓𝑜𝑜𝑒𝑒 𝑓𝑓𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡)𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑝𝑝𝑎𝑎𝑓𝑓𝑎𝑎 𝑝𝑝𝑎𝑎𝑝𝑝 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 ℎ𝑝𝑝𝑜𝑜𝑝𝑝 (𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑐𝑐𝑜𝑜𝑒𝑒𝑑𝑑𝑓𝑓𝑡𝑡𝑓𝑓𝑜𝑜𝑒𝑒) = 𝑝𝑝𝑎𝑎𝑝𝑝 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ𝑡𝑡 𝑇𝑇𝐹𝐹
F-4
AC 25.1309-1B Appendix G APPEN DIX G. ACRONYMS 14 CFR Title 14, Code of Federal Regulations AFM Airplane Flight Manual ALS Airworthiness Limitations Section AMC Acceptable Means of Compliance AMJ Advisory Material Joint ARAC Aviation Rulemaking Advisory Committee ARP Aerospace Recommended Practice ASAWG Airplane-Level Safety Analysis Working Group BCAR British Civil Airworthiness Requirements CMA Common Mode Analysis CCMR Candidate Certification Maintenance Requirement CEA Cascading Events Analysis CMR Certification Maintenance Requirement CSL+1 Catastrophic with Single Latent Plus One EASA European Union Aviation Safety Agency ETOPS Extended Range Twin-engine operations Performance Standards FAA Federal Aviation Administration FHA Functional Hazard Assessment FMEA Failure Modes and Effects Analysis ICA Instructions for Continued Airworthiness JAA Joint Aviation Authorities PRA Particular Risk Analysis PSSA Preliminary System Safety Assessment RTCA RTCA, Inc. (formerly “Radio Technical Commission for Aeronautics”) SAE SAE International (formerly “Society of Automotive Engineers”) SLF Significant Latent Failure SSA System Safety Assessment STC Supplemental Type Certificate TC Type Certificate TSO Technical Standard Order ZSA Zonal Safety Analysis G-1
OMB Control Number: 2120-0746 Expiration Date: 11/30/2024 Advisory Circular Feedback Form
Paperwork Reduction Act Burden Statement: A federal agency may not conduct or sponsor, and a person is not required to respond to, nor shall a person be subject to a penalty for failure to comply with a collection of information subject to the requirements of the Paperwork Reduction Act unless that collection of information displays a currently valid OMB Control Number. The OMB Control Number for this information collection is 2120-0746. Public reporting for this collection of information is estimated to be approximately 20 minutes per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, completing and reviewing the collection of information.
All responses to this collection of information are voluntary FAA Order 1320.46D Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to:
Information Collection Clearance Officer, Barbara Hall, 800 Independence Ave, Washington, D.C. 20590.
If you find an error in this AC, have recommendations for improving it, or have suggestions for new items/subjects to be added, you may let us know by (1) emailing this form to ( ) or (
2) faxing it to the attention of the LOB/SO ( ).
Subject: Date:
Please mark all appropriate line items:
□ An error (procedural or typographical) has been noted in paragraph on page .
□ Recommend paragraph e on pag be changed as follows:
□ In a future change to this AC, please cover the following subject:
(Briefly describe what you want added.)
□ Other comments:
□ I would like to discuss the above. Please contact me.
Submit et d by: Date:
FAA Form 1320-73 ( 09/22) SUPERSEDES PREVIOUS EDITIONS