Appendix 7 Figure A7-3 : Feature Risk Assessment (1/3) 1st step : consider only one hole of the hole feature i and calculate the conditional probability of fracture for this hole.
Anomaly size distribution (App. 2) Crack size versus number of cycle for corner crack “AvsNc” Crack size versus number of cycle for surface crack “AvsNs” Check consistency of size definition between all data
•1st Inspection “cycles since new” distribution + applicable POD curve
•2nd Inspection “cycles since last inspection” distribution + applicable POD curve
•Etc Expected Part certified life Calculate conditional probability of fracture
(see fig. A7-6)
Corner crack conditional prob. of fracture for 1 hole of feature i Keep worst conditional prob.
of fracture Surface crack conditional prob. of fracture for 1 hole of feature i Hole conditional prob. of fracture “hcpf” (1)for 1 hole of feature i (see fig. A7-6) Note :
(1) The term « conditional » means that this probability does not account for the exact anomaly frequency.
Appendix 7 Figure A7-4: Feature Risk Assessment (2/3) 2nd step : Calculate the probability of fracture for one hole by combining the conditional probability of fracture for one hole with the hole actual inner surface area, the applicable manufacturing credits and anomaly frequency correction factor.
prob. of fracture “hcpf” for 1 hole of feature i Determine hole Length / Diameter ratio L/D Fc Determine hole inner surface area (App. 2) S Determine the probability of fracture for 1 hole “hpf” Hpf = hcpf * S * Fc / credit prob. of fracture “hpf” for 1 hole of feature i Determine applicable manufacturing credits (App. 6) credit Determine
applicable
anomaly
frequency
correction factor
“Fc”
(App. 2)
Appendix 7 Figure A7-5: Feature Risk Assessment (3/3) 3rd step : Calculate the risk of fracture for the feature i from the probability of fracture for one hole.
Determine number of holes in the feature i “ni” (App. 5) ni Determine the risk of fracture for the feature i “fr” fr = 1 – (1- hpf)^ni prob. of fracture “hpf” for 1 hole of feature i Feature i risk “fr” 38
Appendix 7 Figure A7-6: Conditional Probability of Fracture Calculation The POF calculation is described here following a Monte Carlosimulation process. A large sample of holes should be simulated (see App. 1, 3 (e)). Each hole simulation in the sample follows the flowchart below to determine if it :
fractures before part certified life / succeeds to reach part certified life / is detected with a crack.
st star artt Is therea manufacturing anomaly?
Success ye Is therea manufacturing anomaly?
Success yes s n noo Notes :
- each r equires a random pick from the pertinent
random variable distribution
-(1) record the number of cycles at fracture or detection for each hole Conditional prob.of fracturebefore Ncycles number of fracturedholes beforeNcycles = total sample size Whatsize « a0 »?
Geta0 anomaly life from “AvsN” curve (see fig. A7-7) Cyclesat inspection(s) ?
Is thereone or more inspection(s) ?
Is anomaly detectable at inspection(s) using applicable PODcurve?
Any inspection during anomaly life ?
Get anomaly size at inspection(s) from “AvsN” curve (see fig. A7-7) Fracture(1) Success Fracture(1) Detection(1) yes no no no yes yes a0anomaly life > part certifiedlife ?
What size « a0 »?
Get a0 anomaly life from “AvsN” curve Cyclesat inspection(s) ?
Is thereone or more inspection(s) ?
Is anomaly detectable at inspection(s) using applicable PODcurve ?
Any inspection during anomaly life ?
Get anomaly size at inspection(s) from “AvsN” curve - Fracture(1) Success Fracture(1) Detection(1) yes no no no yes yes a0 anomaly life > part certifiedlife ?
Appendix 7 Figure A7-7: a0 Anomaly Life & Anomaly Size at Inspection(s) Calculations from “AvsN”Curve a N just above threshold anomaly size inspection a0 anomaly size at inspection a N just above threshold anomaly size inspection a0 anomaly size at inspection A vs N Curve a0 anomaly life 40