Statistical Methods for Probability of Detection in Structural Health Monitoring
There is much interest in the potential to use Structural Health Monitoring (SHM) technology to augment traditional Nondestructive Evaluation (NDE) methods to improve safety, increase asset availability, and reduce maintenance and inspection costs. SHM has the potential to be used in many areas of application including critical components in aircraft and pipelines. Probability of detection (POD) plays a critical role in aircraft structural integrity programs. As such, there has been a high interest in developing methods that can be used to assess POD in SHM applications. In contrast to traditional NDE laboratory experiments to assess POD that involve a set of specimens with cracks, SHM sensors are fixed and SHM data are acquired over time as cracks grow or otherwise evolve. Traditional statistical methods for assessing POD (e.g., as described in MIL-HDBK 1823A 2009) have to be extended to properly handle repeated-measures data. This purpose of this paper is to review the basic statistical concepts of probability of detection (POD) and to show how these concepts can and should be applied to SHM POD studies by modifying and extending existing methods for estimating POD. The methods presented here are applicable when there is a scalar damage index or other response that will be used to make a detect decision. The paper compares a simple model based on length at detection and a random effects model to describe repeated measures data.