AMORE (Advanced MOdelling for Reliability and maintenance Evaluation) is a 2016 exploratory project of the LabEx PERSYVAL-Lab.


For complex systems, maintenance costs represent very often a high proportion of the overall ownership and operating cost. Maintenance actions should then be planned in the best possible way in order to avoid failures at an acceptable cost. An efficient maintenance planning defines when and to which extent the system should be repaired. The environmental conditions and other influencing factors should also be taken into account when seeking for optimal maintenance policies.

Maintenance optimization requires to develop mathematical models which allow to assess the maintained system performance in terms of reliability and availability and to find the best trade-off between preventive and corrective maintenance costs. Different kinds of models are necessary to make optimal maintenance decisions : deterioration models (both at the component and system level), models for the effect of maintenance actions, maintenance policies models. The envisioned breakthroughs within this project towards improved reliability/availability performance and optimal maintenance policies are made possible thanks to advanced probabilistic modeling and statistical treatment of available data to build these different required models.

In this framework, this project aims at providing a platform to initiate a joint work between two teams of PERSYVAL- lab (LJK/FIGAL and GIPSA-lab/SAIGA) - together with one external partner from Troyes University of Technology) - and to prepare more formal and thorough collaborations to address these different key issues in reliability and maintenance modelling in a consistent and comprehensive way.

General model

In this project, we consider an aging system (installation), characterized by its lifetime which is modeled by a probability distribution. Besides the physical aging process, the system suffers from deterioration and other external factors due to the harsh and dynamic environmental conditions in which it operates. The deterioration and the other factors can be seen as covariates impacting the failure intensity and their impact can be modeled similarly to the proportional hazard model. The deterioration and environmental conditions modeling are assumed to be modeled by stochastic processes, either continuous or discrete. When the conditional lifetime distribution of the complex system considering the random factors is derived, then the future behavior of the system is predictable and hence the maintenance operations can be planned.

Maintenance actions are supposed to be imperfect, i.e. after a maintenance the system is not renewed (As Good As New, AGAN) and its failure intensity is only decreased. The corrective maintenances (CM) occur just after a failure. Since their aim is to put, as soon as possible, the system into a state in which it can perform its function again, their effect can be supposed to be As Bad As Old (ABAO). It means that the maintenance action can only render the system failure intensity to be the same as just before failure. Then, a Non Homogeneous Poisson Process (NHPP) is suitable to model the CM times. This process covers a large set of cases and can generate various types of time depending failure intensities. The preventive maintenances (PM) reduce the failure intensity to a level between ABAO and AGAN. Then, virtual age models (Kijima 1989, "Some results for repairable systems with general repair" Journal of Applied Probability) can be used. In these models we distinguish the real age, which is the time elapsed since the system was new, and the virtual age, which describes its present condition when compared to a new system. The virtual age is redefined at failures according to the type of repair performed and it runs along with the true time between repairs.


Once the system’s deterioration/lifetime and the maintenance actions are modeled, the main objective will be to propose an optimal planning of the future maintenance operations, in other words, to optimize the maintenance policy. Based on the modeling assumptions and the available data, we will focus on the following main methodological challenges, that will structure the project research agenda.

  1. Maintenance times, deterioration and environmental conditions modeling by using stochastic processes, 2. Maintenance effect modeling by using virtual age models,
  2. Model calibration using parametric statistical methods,
  3. Failure prediction (prognostics) considering available data (large scale data) (on-line or off line),
  4. Developing optimal maintenance policy (after the last observed maintenance time) for failure prevention,
  5. Maintenance optimization with respect to economic, availability and feasibility constraints.

Some of the project results will be integrated in a software tool, making available the developed models for mainte- nance decision-makers.