Residual life prediction for complex systems with multi-phase degradation by ARMA-filtered hidden Markov model

Zhidong Sheng, Qingpei Hu, Jian Liu, Dan Yu

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The performance of certain critical complex systems, such as the power output of ground photovoltaic (PV) modules or spacecraft solar arrays, exhibits a multi-phase degradation pattern due to the redundant structure. This pattern shows a degradation trend with multiple jump points, which are mixed effects of two failure modes: a soft mode of continuous smooth degradation and a hard mode of abrupt failure. Both modes need to be modeled jointly to predict the system residual life. In this paper, an autoregressive moving average model-filtered hidden Markov model is proposed to fit the multi-phase degradation data with unknown number of jump points, together with an iterative algorithm for parameter estimation. The comprehensive algorithm is composed of non-linear least-square method, recursive extended least-square method, and expectation–maximization algorithm to handle different parts of the model. The proposed methodology is applied to a specific PV module system with simulated performance measurements for its reliability evaluation and residual life prediction. Comprehensive studies have been conducted, and analysis results show better performance over competing models and more importantly all the jump points in the simulated data have been identified. Also, this algorithm converges fast with satisfactory parameter estimates accuracy, regardless of the jump point number.

Original languageEnglish (US)
Pages (from-to)19-35
Number of pages17
JournalQuality Technology and Quantitative Management
Issue number1
StatePublished - Jan 2 2019


  • System reliability
  • hidden Markov model
  • multi-phase degradation
  • residual life prediction

ASJC Scopus subject areas

  • Business and International Management
  • Industrial relations
  • Management Science and Operations Research
  • Information Systems and Management
  • Management of Technology and Innovation


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