A mixture frailty model for maintainability analysis of mechanical components: a case study

  • Rezgar Zaki
  • Abbas BarabadiEmail author
  • Ali Nouri Qarahasanlou
  • A. H. S. Garmabaki
Original Article


Knowing the maintainability of a component or a system means that repair resource allocations, such as spare part procurement and maintenance training, can be planned and optimized more effectively. Repair data are often collected from multiple and distributed units in different operational conditions, which can introduce heterogeneity into the data. Part of such heterogeneity can be explained and isolated by the observable covariates, whose values and the way that they can affect the item’s maintainability are known. However, some factors which may affect maintainability are typically unknown (unobserved covariates), leading to unobserved heterogeneity. Nevertheless, many researchers have ignored the effect of observed and un-observed covariates, and this may lead to erroneous model selection, as well as wrong conclusions and decisions. Moreover, many authors have simplified their analysis by considering a complex system as a single item. In these studies, the assumption is that all repair data represent an identical repair process for the item. In practice, mechanical systems are composed of multiple parts, with various failure mechanisms, which need different repair processes (repair modes) to return to the operational phase; classical distribution, such as lognormal, which is only a function of time, may not be able to model such complexity. The paper utilizes the mixture frailty model (MFM) in the presence of some specific observed or unobserved covariates to predict maintainability more precisely. MFMs can model the effect of observed and unobserved covariates, as well as identifying different repair processes in the repair dataset. The application of the proposed model is demonstrated by a case study.


Mixture Weibull Failure model Repair process Covariates Repair time Maintainability Frailty model 



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Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.Department of Technology and SafetyUiT The Arctic University of NorwayTromsøNorway
  2. 2.Faculty of Mining Engineering, Petroleum and GeophysicsShahrood University of TechnologyShahroodIran
  3. 3.Division of Operation and Maintenance EngineeringLuleå University of TechnologyLuleåSweden

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