Statistical Maintenance Modeling

Hoang Pham, Wenjian Li

Research output: Chapter in Book/Report/Conference proceedingChapter


The first part of this chapter provides a brief introduction to statistical maintenance modeling subject to multiple failure processes. It includes a description of general probabilistic degradation processes. The second part discusses detailed reliability modeling for degraded systems subject to competing failure processes without maintenance actions. A generalized multi-state degraded-system reliability model with multiple competing failure processes including degradation processes and random shocks is presented. The operating condition of the multi-state system is characterized by a finite number of states. A methodology to generate the system states when multi-failure processes exist is also discussed. The model can be used not only to determine the reliability of the degraded systems in the context of multi-state functions but also to obtain the probabilities of being in a given state of the system. The third part describes the inspection–maintenance issues and reliability modeling for degraded repairable systems with competing failure processes. A generalized condition-based maintenance model for inspected degraded systems is discussed. An average long-run maintenance cost rate function is derived based on an expression for degradation paths and cumulative shock damage, which are measurable. An inspection sequence is determined based on the minimal maintenance cost rate. Upon inspection, a decision will be made on whether to perform preventive maintenance or not. The optimum preventive maintenance thresholds for degradation processes and inspection sequences are also determined based on a modified Nelder–Mead downhill simplex method. The fourth part briefly discusses some dependent competing risk models with various applications subject to multiple degradation processes and random shocks especially using time-varying copulas. Finally, the last part is given over to the conclusions and a discussion of future perspectives for degraded-system maintenance modeling.

Original languageEnglish (US)
Title of host publicationSpringer Handbooks
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages26
StatePublished - 2023
Externally publishedYes

Publication series

NameSpringer Handbooks
ISSN (Print)2522-8692
ISSN (Electronic)2522-8706

All Science Journal Classification (ASJC) codes

  • General


  • Competing risks
  • Compound Poisson process
  • Degradation process
  • Maintenance policy
  • Preventive maintenance


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