A framework for predicting the remaining useful life of a single unit under time-varying operating conditions

Haitao Liao, Zhigang Tian

Research output: Contribution to journalArticlepeer-review

128 Scopus citations


Product reliability in the field is important for a wide variety of critical applications such as manufacturing, transportation, power generation, and health care. In particular, the propensity of achieving zero-downtime emphasizes the need for Remaining Useful Life (RUL) prediction for a single unit. The task is quite challenging when the unit is subject to time-varying operating conditions. This article provides a framework for predicting the RUL of a single unit under time-varying operating conditions by incorporating the results of both accelerated degradation testing and in situ condition monitoring. For illustration purposes, the underlying degradation process is modeled as a Brownian motion evolving in response to the operating conditions. The model is combined with in situ degradation measurements of the unit and the operating conditions to predict the unit's RUL through a Bayesian technique. When the operating conditions are piecewise constant, statistical approaches using a conjugate prior distribution and Markov chain Monte Carlo approach are developed for cases involving linear and non-linear degradation-stress relationships, respectively. The proposed framework is also extended to handle a more complex case where the projected future operating conditions are stochastic. Simulation experiments and a case study for ball bearings are used to verify the prediction capability and practicality of the framework. In the case study, a quantile regression technique is proposed to handle load-dependent failure threshold values in RUL prediction.

Original languageEnglish (US)
Pages (from-to)964-980
Number of pages17
JournalIIE Transactions (Institute of Industrial Engineers)
Issue number9
StatePublished - Sep 1 2013
Externally publishedYes


  • Accelerated degradation testing
  • Bayesian updating
  • remaining useful life

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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