Impact of Multiple On-Board Inspections on Cumulative Probability of Detection

Abstract

The impending application of on-board sensors for detecting and sizing material defects and evaluating their consequences will lead to improved forecasting of readiness, as well as improved safety, retirement-for-cause, and management of assets. This research looks at the consequences of multiple, i.e., continual, on-board inspections on the cumulative probability of detection (CPOD) of the system; that is the probability of detecting a defect considering all previous inspections. In particular, modeling and simulation of the CPOD is examined as a function of the degree of correlation between subsequent inspections. A surface crack in a turbine disk is used as a test case with loading from a typical stress spectrum from a fighter engine. The analysis indicates that a significant difference in detectability is achieved through multiple inspections depending upon the degree of correlation between inspections, with statistically independent inspections exhibiting a “dramatically” improved CPOD over dependent inspections. In particular, if each inspection is statistically independent 1) it is the left tail of the parent POD that defines the CPOD, 2) for the same median value, a higher coefficient of variation of the parent POD generates a significantly more effective CPOD, and 3) if enough inspections are performed, the CPOD curve becomes a step function at the first non-zero value in the parent POD curve, thereby giving orders-of-magnitude improvement in detectibility over the parent POD. The critical issue of statistical independence of multiple inspections is investigated by examining the CPOD as a function of correlation between inspections. The results indicate that the effectiveness of continual inspections on the CPOD varies from a correlation coefficient of zero (independent), which gives a dramatic improvement compared to the parent POD, to a correlation coefficient of one (dependent), which reverts to the parent POD. In summary, the correlation between inspections is a critical component that determines the effectiveness of continual inspections.