A Deconvolution Approach for Degradation Modeling With Measurement Error

Abstract

Degradation trajectories over time provide information that is important for the life estimation of products and systems. However, most of the time the degradation measurements are disturbed by different conditions that cause uncertainty. This is an important problem in the area of reliability assessment based on degradation data, because the multiple observed measurements characterize the degradation path, which ends defining a failure time. Thus, in the presence of measurement error the observed failure time may be different from the true failure time. As the measurement error is inherent to the degradation testing, it results important to establish models that allow to obtain the true degradation from the observed degradation and some measurement error. In this article, a modeling approach to assess reliability under measurement error is proposed. It is considered that the true degradation is obtained by deconvoluting the observed degradation and the measurement error. We considered the inverse Gaussian and Wiener processes to describe the observed degradation of a particular case study. Then, the obtaining of the true degradation is performed by developing the proposed deconvolution method which considers that the measurement error follows a Gaussian distribution. An illustrative example is presented to implement the proposed modeling, and some important insights are provided about the reliability assessment.

Keywords

• Deconvolution
• fast Fourier transform
• inverse Gaussian process
• measurement error
• reliability
• Wiener process