Degradation modeling considering unit-to-unit heterogeneity-A general model and comparative study

Zhijie Wang, Qingqing Zhai*, Piao Chen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)
14 Downloads (Pure)


The performance of units in the same batch can exhibit considerable heterogeneity due to the variation in the raw materials and fluctuation in the manufacturing process. For products suffering performance degradation in their use, such heterogeneity often results in an increase in the dispersion of the degradation paths of units in a population. The degradation rate of products can be unit-specific and often treated as random effects. This paper develops a novel random-effects Wiener process model to account for the unit-to-unit heterogeneity in the degradation, where the generalized inverse Gaussian (GIG) distribution is used to model the unit-specific degradation rate. The GIG distribution is a very general distribution with broad applications, which includes the inverse Gaussian (IG) distribution and the Gamma distribution as special cases. We investigate the model properties and develop an expectation maximization (EM) algorithm for parameter estimation. By comparing the proposed model with existing models on two real degradation datasets of the infrared LEDs and the GaAs lasers, we show that the proposed model is quite effective for degradation modeling with heterogeneous rates.

Original languageEnglish
Article number107897
Number of pages10
JournalReliability Engineering and System Safety
Publication statusPublished - 2021

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • EM algorithm
  • Generalized inverse Gaussian distribution
  • Heterogeneous degradation
  • Wiener process model


Dive into the research topics of 'Degradation modeling considering unit-to-unit heterogeneity-A general model and comparative study'. Together they form a unique fingerprint.

Cite this