### Modeling of The Effect of Corrective and Preventive Maintenance with Bathtub Failure Intensity

*Makrem Krit, Abdelwaheb Rebaï*

**Abstract**: The aim of this paper is to propose a general model to illustrate the joint effect of corrective and preventive maintenance on repairable systems. The intensity of the failure process without maintenance is characterized in bathtub form. The maintenance effect is expressed by the change induced on the failure intensity before and after maintenance. It takes into account the possibility of dependent maintenance times with different effects. The likelihood functions are derived, so parameter estimations and assessment of the maintenance efficiency are possible. The properties of the parameters estimators have to be theoretically studied. Finally, results are applied to a real maintenance data set.

**Keywords**: Bathtub failure intensity; Estimation; Imperfect maintenance; Reliability; Repairable system

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