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ABSTR ACT
This paper presents a methodology for extending
probability of detection (POD) modeling for
continuously valued (â vs. a) signal responses to
allow for the addition of multiple variables beyond
the simple discontinuity size model, along with
higher-level interactions. The statistical methodology
for correctly transforming these more complex
linear models into POD curves is provided, and the
approach is illustrated with a simulated dataset that
includes polynomial and categorical predictors.
KEYWORDS: probability of detection, linear regression,
â versus a, eddy current
1. Introduction
Probability of detection (POD) modeling is a useful tool for
assessing the detection capability of a nondestructive evalu-
ation (NDE) inspection system. Structural components that
may experience fatigue during normal use can be periodically
reinspected to find discontinuities so that any defects can
be repaired or replaced before growing to dangerous sizes.
These inspection intervals are chosen based on the inspec-
tion system’s capability. POD considers false detection, but it
focuses on true detection and an inspection system’s capa-
bility to find discontinuities before they reach a critical size.
An inspection system that finds small discontinuities is of less
interest than one that consistently finds all the large disconti-
nuities. Inspection systems prone to missing large discontinu-
ities will require more frequent reinspection [1–5].
Often, variables other than the discontinuity size can affect
the nondestructive inspection response. Current methods and
software [6, 7] for POD modeling do not support this. Some
prior work has considered additional parameters in â versus
a signal-response analysis. Improved model fits have been
achieved by considering additional parameters such as discon-
tinuity depth, alongside discontinuity length, for representing
signals from surface discontinuities using eddy current testing
[8–10]. Concepts of multifactorial designed experiments and
multiple linear regression (MLR) for nondestructive testing
reliability evaluation were discussed by Müller and Öberg [11,
12], but no applications with data were presented. In another
study, a multi-parameter linear regression model was fit to
experimental vibration-based structural health monitoring
data and used to evaluate POD for varying measurement
locations and degradation over time [13]. This work used a
Monte Carlo approach to generate POD estimates, but it did
not present much detail on the model form or consideration of
higher-order terms. Smart et al. [14] considered a multivariate
regression model for pipe material characterization perfor-
mance, but this model was not extended to POD evaluation.
In other work [15], a Bayesian approach was successfully used
to model 11 additional variables, and although this method
provided POD estimates, it did not provide a functional form.
This paper extends current signal-response models for
POD to include additional categorical and higher-order
response variables. It was inspired by a large bolt-hole eddy
MULTIVARIATE PROBABILITY OF DETECTION
MODELING INCLUDING CATEGORICAL
VARIABLES AND HIGHER-ORDER RESPONSE
MODELS
CHRISTINE E. KNOTT†*, CHRISTINE SCHUBERT KABBAN‡, AND JOHN C. ALDRIN§
† Materials and Manufacturing Directorate, Air Force Research Laboratory,
Wright-Patterson AFB, OH 45433
‡ Department of Mathematics and Statistics, Air Force Institute of Technology,
Graduate School of Engineering and Management, Wright-Patterson AFB, OH
45433
§ Computational Tools, Gurnee, IL 60031
*Corresponding author: christine.knott.1@us.af.mil
Materials Evaluation 83 (8): 57–72
https://doi.org/10.32548/2025.me-04532
©2025 American Society for Nondestructive Testing
NDTTECHPAPER
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