A Gamma Process Based Degradation Model with Fractional
Gaussian Noise
Xiangyu Wang
1
, Xiaopeng Xi
2
, and Marcos E. Orchard
3
1
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong,
266590, China
202181080010@sdust.edu.cn
2
Advanced Center for Electrical and Electronic Engineering, Universidad T
´
ecnica Federico Santa Mar
´
ıa, Valpara
´
ıso,
Chile
xi.xiaopeng@usm.cl (corresponding author)
3
Department of Electrical Engineering, Faculty of Mathematical and Physical Sciences, Universidad de Chile,
Santiago, Chile
morchard@ing.uchile.cl
ABSTRACT
In modern industrial and engineering systems, stochastic
degradation models are widely used for reliability analysis
and maintenance decision-making. However, due to imper-
fect sensors and environmental influences, it is difficult to
directly observe the latent degradation states. Traditional
degradation models typically assume that measurement er-
rors have simple statistical properties, but this assumption
often does not hold in practical applications. To address
this issue, this paper constructs a degradation model based
on the Gamma process (GP) and assumes that measure-
ment noise can be characterized by the fractional Gaussian
noise (FGN). Furthermore, this paper proposes a method
combining Gibbs sampling with the stochastic expectation-
maximization (SEM) algorithm to achieve efficient estima-
tion of the model parameters and accurate inference of the
latent degradation states. Simulation results demonstrate that
the proposed model, validated solely through numerical sim-
ulations, exhibits improved generalizability compared to the
GP model with Gaussian noise.
1. INTRODUCTION
Prognostics and health management (PHM) aims to utilize
data analysis and monitoring techniques to predict the degra-
dation of system components or equipment, and to implement
appropriate maintenance measures to ensure their reliability
and safety (Gebraeel et al., 2023; Xi et al., 2018). In recent
years, this technology has gained widespread attention be-
cause it not only reduces maintenance costs but also improves
Xiangyu Wang et al. This is an open-access article distributed under the
terms of the Creative Commons Attribution 3.0 United States License, which
permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original author and source are credited.
system reliability (Liu et al., 2023). The collected data for
predicting the future degradation behavior is typically clas-
sified into two categories: (1) event data and (2) condition
monitoring (CM) data. However, collecting sufficient event
data can be costly, and in addition, some systems rarely expe-
rience failure events (Hong et al., 2022). With the continuous
improvement of data preprocessing techniques, CM data can
help analyze the health status and performance degradation
of systems (Xi et al., 2020). Simultaneously, the degradation
state is typically represented by CM data.
In practical applications, systems often involve various uncer-
tain factors both in their internal characteristics and external
environment. In the presence of such uncertainty, stochas-
tic processes demonstrate significant advantages. In the se-
lection of degradation models, the GP is commonly used to
model systems with monotonic increments of degradation.
For example, the GP has been applied to model the degra-
dation of rolling element bearings, assessing the approxi-
mate failure time distribution when crack size exceeds a cer-
tain threshold (Wang et al., 2021). Additionally, accelerated
degradation tests have been proposed to efficiently obtain re-
liable degradation information for light-emitting diodes (Ling
et al., 2014). To address different failure mechanisms, a GP-
based method has been developed for extrapolating failure
times in high-reliability products (Li et al., 2022). The afore-
mentioned studies obtained the failure time distribution at a
given threshold through approximate methods, and interested
readers can refer to review articles for more details (Li et al.,
2024).
It is noteworthy that degradation measurements are often in-
fluenced by sensor accuracy and external environmental inter-
ference, resulting in the true degradation state being obscured
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