A Generalized Wiener Process Degradation Model with Two Transformed Time Scales

Zhihua Wang, Junxing Li, Xiaobing Ma*, Yongbo Zhang, Huimin Fu, Sridhar Krishnaswamy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Degradation analysis is very useful in reliability assessment for complex systems and highly reliable products, because few or even no failures are expected in a reasonable life test span for them. In order to further our study on degradation analysis, a novel Wiener process degradation model subject to measurement errors is proposed. Two transformed time scales are involved to depict the statistical property evolution over time. A situation where one transformed time scale illustrates a linear form for the degradation trend and the other transformed time scale shows a generalized quadratic form for the degradation variance is discussed particularly. A one-stage maximum likelihood estimation of parameters is constructed. The statistical inferences of this model are further discussed. The proposed method is illustrated and verified in a comprehensive simulation study and two real applications for indium tin oxide (ITO) conductive film and light emitting diode (LED). The Wiener process model with mixed effects is considered as a reference. Comparisons show that the proposed method is more general and flexible, and can provide reasonable results, even in considerably small sample size circumstance.

Original languageEnglish (US)
Pages (from-to)693-708
Number of pages16
JournalQuality and Reliability Engineering International
Issue number4
StatePublished - Jun 2017


  • Wiener process model
  • measurement error
  • one-stage parameter estimation
  • performance degradation
  • transformed time scale

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research

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