Semiparametric Models for Accelerated Destructive Degradation Test Data Analysis

Abstract

Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials' long term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition.Motivated by this challenge, we propose a semi-parametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonically decreasing).Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and accelerating variable, allowing for extrapolation to the use conditions. We develop an efficient procedure to estimate model parameters. We also use simulation to validate the developed procedures and demonstrate the robustness of the semi-parametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications.

ADDT: An R Package for Analysis of Accelerated Destructive Degradation Test Data

“…In (6), g(·) is a monotonically decreasing function modeled by splines with parameter vector γ. See Xie et al [7] for more details on the semiparametric method. As a more flexible method designated to a wide variety of materials, the nonparametric component is used to build the baseline degradation path.…”

“…In most applications, an ADDT dataset typically includes degradation measurements under different measuring time points, and accelerating variables such as temperature and voltage. In the ADDT package, there are four publicly available datasets ready for users to do analysis, which are the Adhesive Bond B data in [4], the Seal Strength data in [5], the Polymer Y data in [6], and the Adhesive Formulation K data in [7]. Users can load those datasets by downloading, installing the package ADDT and appropriately calling the data function.…”

Big data and reliability applications: The complexity dimension

“…Zhou, Serban, and Gebraeel (2011) and Zhou et al (2014) used functional data analysis techniques to model the degradation paths. For destructive degradation test data, Xie et al (2018) developed a semiparametric model to describe the degradation path. For products and systems used in the field, the units are typically subject to time-varying usage and environmental conditions.…”

Statistical Methods for Thermal Index Estimation Based on Accelerated Destructive Degradation Test Data

“…Due to the nature of the testing, ADDT is a commonly used technique for evaluating long-term performance of polymeric materials. Examples of ADDT data includes the Adhesive Bond B data in [2], the Polymer data in [3], the Seal Strength data in [4], and the Formulation K data in [5].…”

“…In the statistical literature, the parametric method is also commonly used to model the ADDT data, and the ML method is used for parameter estimation. Recently, a semiparametric method is proposed to analyze ADDT data in Xie et al [5]. The basic idea of the semiparametric method is to use monotonic splines to model the baseline degradation path and use a parametric method to model the effect of accelerating variable.…”