Int J Performability Eng ›› 2022, Vol. 18 ›› Issue (7): 521-528.doi: 10.23940/ijpe.22.07.p7.521528

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Modelling the Maintenance of Complex Repairable Systems based on Reliability by Comparing the Proportional Intensity Model and the Generalized Proportional Intensity Model

Houssam Lala*, Sidali Bacha, Ahmed Bellaouar, and Redouane Zellagui   

  1. Transport Engineering and Environment Laboratory, Frères Mentouri Constantine 1 University, Constantine, 25000, Algeria
  • Submitted on ; Revised on ; Accepted on
  • Contact: * E-mail address:

Abstract: This work focuses on modeling the maintenance of complex repairable systems (CRS) based on realistic models to highlight the effect of imperfect repairs (IR) on the future performance of the system while incorporating certain information concomitants of the system called covariates. The latter were considered, thanks to the Generalized Proportional Intensity Model (GPIM), for a history of reliability and maintenance of a turbocharger having operated for nearly nine years in the National oil and gas company (SONATRACH). The GPIM was compared with the Proportional Intensity Model (PIM) to show its flexibility to take, in addition to covariates, the effect of corrective and preventive maintenance actions. The estimation of the model parameters is ensured by the maximum likelihood approach (MLE) using the MATLAB programming language. The goodness of fit of the models can be ensured by the likelihood test (LR) using the results found by the maximum likelihood approach. The failure intensity functions of the two models consider the linear log law, based on the non-homogeneous Poisson process (NHPP), with the same covariates “programming of maintenance shutdowns”, “temperature” and “time between failures’’.

Key words: repairable complex systems, covariates, proportional intensity model (PIM), generalized proportional intensity model (GPIM), Inhomogeneous Poisson process (NHPP), maximum likelihood approach (MLE), the likelihood ratio (LR)