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.
Highlights
The degradation modeling has become an important tool in the area of reliability inference of highly reliable products
One of the main reasons is because as modern products and systems are developed with high quality standards the traditional reliability analysis approach based on failure times has become unsuitable, this has posed the need of alternative models
Physics-based models and multi-state models. These four approaches consist in finding the model that describes the process of degradation, determining the failure time when the degradation accumulates to a certain critical level, characterize the failure time distribution, and perform the reliability assessment
Summary
The degradation modeling has become an important tool in the area of reliability inference of highly reliable products. The distribution of a true measurement is obtained by deconvoluting the characteristic functions of the distribution of the observed measurement and a kernel of the error distribution [31]–[35] These models do not involve a stochastic modeling as is the case when dealing with degradation processes, which is one of the contributions of this article. In the case of the Wiener process, the reliability assessment is provided with the first-passage time distributions From both cases, it is observed that the reliability assessment of the product is miss-estimated if the ME is not considered in the modeling. The deconvolution approach is considered given that the true measurements in degradation analysis are not observed directly, which means that they represent a hidden state of the degradation process.
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