University of Texas at San Antonio Harry Millwater and Brian Shook Dept. of Mechanical Engineering University of Texas at San Antonio Steve Hudak, Mike Enright, Loren Francis Southwest Research Institute AFRL DUS&T Program Pat Golden, Program Manager AFOSR Prognosis Workshop Feb 19-20, 2008 Cincinnati, OH Impact of Multiple On-Board Inspections on Cumulative Probability of Detection

University of Texas at San Antonio Case Study  3 Median POD Values  200 Mil  400 Mil  600 Mil  32% Coefficient of Variation  30 Mil POD  32% Coefficient of Variation Which is more effective at reducing the probability of failure? Continual Inspections Depot Inspection

University of Texas at San Antonio Case Study Example problem –Surface crack at bore (defined by pdf) –Loading from air-to-ground mission from F100- PW-229 engines –POD curve modeled with lognormal distribution –FAA library indicates a COV of 32% for ultrasonic inspection –Vary median of POD curve –One inspection per flight

University of Texas at San Antonio Inspection Simulation POD Curve P* a* Detected Cracks

University of Texas at San Antonio Results Independent inspections POD: median 600 mils COV 32%

University of Texas at San Antonio Inspection Simulation dependentindependent

University of Texas at San Antonio Frequency of Inspection Parent POD (600/0.32)

University of Texas at San Antonio Effect of Multiple Independent Inspections Note, even if POD = 0.01 for a single inspection: –after 1000 independent inspections the cumulative POD is –after 1000 dependent inspections the cumulative POD is 0.01

University of Texas at San Antonio Supporting Publication “Quantifying the Effects of Redundant Fluorescent Penetrant Inspection,” –Kimberly Erland, Pratt & Whitney, West Palm Beach, Review of progress in quantitative nondestructive evaluation, Vol. 8B,1988, pp –“The fluorescent penetrant inspection process is not independent inspection-to-inspection and therefore the probability of detection for redundant FPI cannot be obtained by a simple multiplication of probabilities Conclusions substantiated using actual inspection data

University of Texas at San Antonio Air-to-Ground Results No Inspection Single Mid-Life Inspection Continual Inspection Dependent Inspections

University of Texas at San Antonio Air-to-Ground Results No Inspection Single Mid-Life Inspection Continual Inspection Dependent Inspections

University of Texas at San Antonio Air-to-Ground Results Continual Inspection Single Mid-Life Inspection No Inspection Dependent Inspections

University of Texas at San Antonio Last Inspection a crit a last A Priori Estimation of POD Effectiveness For continual dependent inspections, POD(a crit ) determines the amount of reduction in POF regardless of the shape of the POD curve and the crack growth curve.

University of Texas at San Antonio Effect of POD(a crit ) POD(a crit ) = 70% for all POD curves Critical crack size ~ 600 mils

University of Texas at San Antonio Normalized Results POF Reduced = 1-POD(a crit ) = 0.3 for all POD curves

University of Texas at San Antonio Random a crit If a crit is random, say from stress scatter or fracture toughness variation, the effective reduction in POF can be determined by Conditional Expectation

University of Texas at San Antonio Lessons Learned Model recurring inspections as dependent - conservative approach POD(a crit ) defines effectiveness of continual inspections

University of Texas at San Antonio Conclusions Continual inspections with a coarse POD sensitivity can offer advantages in the reduction of POF with respect to a more accurate depot inspection - even with dependent inspections.

University of Texas at San Antonio Food for Thought POD curve still useful to characterize the inspection process for recurring inspections? Focus should be on characterizing POD(a crit ) and it’s scatter a crit

University of Texas at San Antonio Questions

University of Texas at San Antonio Inspection Simulation POD (a(N)) Crack is detected for sensor realization n inspection j POD(  (N i )) NiNi POD(a * j ) Realization n S j generates a sensor with detectible crack size (DCS) = n a * j This sensor will detect a crack larger than n a * j or, equivalently, POD(a(N i ))  POD( n a * j ) Process is repeated with independent realizations

University of Texas at San Antonio Subsequent Inspections For subsequent inspections, n a DCS should be approximately the same for each sensor, n a DCS(j)  n a DCS(j+1) This can be simulated by generating samples for subsequent inspections that are correlated to the first inspection. A correlation coefficient of 1.0 implies dependent inspections, i.e., n a DCS(1) = n a DCS(j)

University of Texas at San Antonio Inspection Simulation POD(300) = 0.18 POD with median = 400 miles, COV=32% 18% of sensors will detect a defect less than 300 mils

University of Texas at San Antonio Independent Assumption CPOD X1 X2 Inspection i Inspection i+1 Each inspection significantly increases the CPOD

University of Texas at San Antonio Dependent Assumption Inspection i Inspection i+1 CPOD X1 X2 Each inspection encapsulates previous inspection CPOD=POD(i+1)

University of Texas at San Antonio Effects of POD Curve Median POD # Fail# Detected # Would Fracture POF wo inspection POF w inspection E E E E E-21.03E E-27.5E-3

University of Texas at San Antonio Cumulative POD Cumulative POD based on the assumption of independent inspections (one minus the probability of missing it at all previous inspections) where a i is the crack size at inspection i, POD(a) is the applied POD curve

University of Texas at San Antonio Scatter of Parent POD Larger COV of parent POD leads to significantly higher cumulative POD POD Median: 600 mils Larger COV Independent Inspections

University of Texas at San Antonio CPOD vs. Median and COV of Parent POD Cumulative POD = 1 Cumulative POD = 0 Independent Inspections Cumulative POD varies rapidly wrt COV of parent POD

University of Texas at San Antonio Multiple Sensors CPOD Corr=1 CPOD Corr=0 1 Sensor Bounds

University of Texas at San Antonio Multiple Sensors 1 Sensor Same Sensor Corr=0.9 1 Sensor

University of Texas at San Antonio Multiple Sensors Same Sensor Corr=0.9 Multiple Sensors Corr=0.5 1 Sensor 2 Sensors

University of Texas at San Antonio Multiple Sensors 1 Sensor 2 Sensors 3 Sensors Same Sensor Corr=0.9 Multiple Sensors Corr=0.5

University of Texas at San Antonio Multiple Sensors 1 Sensor 2 Sensors 3 Sensors 10 Sensors Same Sensor Corr=0.9 Multiple Sensors Corr=0.5

University of Texas at San Antonio Effect of Correlation on CPOD Corr=1 Corr=0.8 Corr=0 Corr=0.2 Corr=0.4 Corr=0.6