Degradation data analysis based on a generalized Wiener process subject to measurement error

Junxing Li, Zhihua Wang*, Yongbo Zhang, Huimin Fu, Chengrui Liu, Sridhar Krishnaswamy

*Corresponding author for this work

Research output: Contribution to journalArticle

24 Scopus citations


Wiener processes have received considerable attention in degradation modeling over the last two decades. In this paper, we propose a generalized Wiener process degradation model that takes unit-to-unit variation, time-correlated structure and measurement error into considerations simultaneously. The constructed methodology subsumes a series of models studied in the literature as limiting cases. A simple method is given to determine the transformed time scale forms of the Wiener process degradation model. Then model parameters can be estimated based on a maximum likelihood estimation (MLE) method. The cumulative distribution function (CDF) and the probability distribution function (PDF) of the Wiener process with measurement errors are given based on the concept of the first hitting time (FHT). The percentiles of performance degradation (PD) and failure time distribution (FTD) are also obtained. Finally, a comprehensive simulation study is accomplished to demonstrate the necessity of incorporating measurement errors in the degradation model and the efficiency of the proposed model. Two illustrative real applications involving the degradation of carbon-film resistors and the wear of sliding metal are given. The comparative results show that the constructed approach can derive a reasonable result and an enhanced inference precision.

Original languageEnglish (US)
Pages (from-to)57-72
Number of pages16
JournalMechanical Systems and Signal Processing
StatePublished - Sep 15 2017


  • Degradation analysis
  • Maximum likelihood estimation
  • Measurement errors
  • Wiener process

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications

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