Abstract: The complex industrial system, which is subject to different influencing factors, often manifests itself in several failure modes, making the use of different standard and unimodal distributions to model its behavior unnecessary and inappropriate. In this article, we are interested in presenting an approach to modeling the dynamic behavior of the system based on a Mixture Weibull Proportional Hazard Model. In addition to the advantage of proportional hazard models taking into account the influence of covariates on system behavior, the use of mixed Weibull models makes it possible, on the basis of a mixing parameter W_i, to highlight the weight of each component i on the overall and dynamic behavior of the system. This approach is illustrated first by considering data generated by the MATLAB programming language by justifying the contribution that can be obtained by this mixture model in the modeling of the reliability of complex systems. Then, from a history of maintenance and reliability of a gas turbine having operated for more than thirteen years in the SONATRACH company, the maximum likelihood approach and the likelihood ratio test makes it possible to validate the goodness of fit of the proposed model and to estimate the influence in the probabilities of failures of two heterogeneous subpopulations representing hidden behaviors. Then, the mixed Weibull model will be extended to incorporate other covariates of the system by constructing the proportional hazard model (PHM). The proposed model is validated by the Akaike Information Criterion (AIC) and the Bayes information criterion (BIC) based on the maximum likelihood value. This approach facilitates decision-making on system intervention, taking into account operating conditions and prioritizing the most critical subsystem over time.

Key words: mixture Weibull proportional hazard model, covariates, mixing parameter Wi, maximum likelihood approach, likelihood ratio test, heterogeneous subpopulations