Statistical Methods for Estimating Probability of Detection in Structural Health Monitoring
Abstract
There is much interest in the potential to use structural health monitoring (SHM) technology to augment traditional nondestructive inspection (NDI) methods to improve safety, increase asset availability, and reduce maintenance and inspection costs. SHM has the potential to be used in many applications, including critical components in aircraft and pipelines. Probability of detection (POD) plays a critical role in aircraft structural integrity programs, leading to increased interest in developing methods to assess POD in SHM applications. In contrast to traditional NDI laboratory experiments involving specimens with cracks, SHM sensors are fixed, and SHM data are acquired over time as cracks grow or otherwise evolve. Thus, traditional statistical methods for assessing POD must be replaced or extended to properly handle repeated-measures data. The purpose of this paper is to review the basic statistical concepts of POD and show how these concepts can be extended or adapted for SHM-POD applications. The paper presents statistical methods for modifying and extending existing POD methods, including a simple size-of-damage-at-detection (SoDaD) method and a random-parameter (RP) method for repeated-measures data. The methods are compared using three case studies involving Piezoelectric Transducer (PZT), Carbon Nanotube (CNT), and Comparative Vacuum Monitoring (CVM) sensor systems. Results show that the SoDaD method provides a simple approach for POD estimation with limited data, while the RP method offers enhanced modeling fidelity by utilizing repeated measurements. These methods are applicable when a scalar damage index or similar response is used to make a detection decision.
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BibTeX
@misc{xia2026statistical,
title = {{Statistical Methods for Estimating Probability of Detection in Structural Health Monitoring}},
author = {Qizheng Xia and William Q. Meeker and Dennis Roach and Seth S. Kessler and Qing Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28407},
eprint = {2609.28407},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28407},
}
RIS
TY - UNPB
TI - Statistical Methods for Estimating Probability of Detection in Structural Health Monitoring
AU - Qizheng Xia
AU - William Q. Meeker
AU - Dennis Roach
AU - Seth S. Kessler
AU - Qing Li
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28407
UR - https://arxiv.org/abs/2609.28407
AB - There is much interest in the potential to use structural health monitoring (SHM) technology to augment traditional nondestructive inspection (NDI) methods to improve safety, increase asset availability, and reduce maintenance and inspection costs. SHM has the potential to be used in many applications, including critical components in aircraft and pipelines. Probability of detection (POD) plays a critical role in aircraft structural integrity programs, leading to increased interest in developing methods to assess POD in SHM applications. In contrast to traditional NDI laboratory experiments involving specimens with cracks, SHM sensors are fixed, and SHM data are acquired over time as cracks grow or otherwise evolve. Thus, traditional statistical methods for assessing POD must be replaced or extended to properly handle repeated-measures data. The purpose of this paper is to review the basic statistical concepts of POD and show how these concepts can be extended or adapted for SHM-POD applications. The paper presents statistical methods for modifying and extending existing POD methods, including a simple size-of-damage-at-detection (SoDaD) method and a random-parameter (RP) method for repeated-measures data. The methods are compared using three case studies involving Piezoelectric Transducer (PZT), Carbon Nanotube (CNT), and Comparative Vacuum Monitoring (CVM) sensor systems. Results show that the SoDaD method provides a simple approach for POD estimation with limited data, while the RP method offers enhanced modeling fidelity by utilizing repeated measurements. These methods are applicable when a scalar damage index or similar response is used to make a detection decision.
ER -