The functions of the passive B systems are based on thermal-hydraulic (T-H) principles, which are not currently considered to be subject to any kind of failure. But due to the environment and to the physical phenomena that may deviate from expectation, the passive system may fail to meet its required passive function. The quantification of the T-H unreliability is often still a difficult process due to the numerous uncertainties. The objective of the project is to propose a specific methodology to assess the passive system thermal-hydraulic reliability. The methodology is tested on an example of industrial T-H passive system. The T-H calculations are performed using the RELAP5, ATHLET and CATHARE computer codes. The RMPS project is a cost-shared action started on February 2001 and with duration of three years. In this paper we will present the work program insisting on the innovative aspects and we will describe the example of passive system chosen to test the methodology. Due to the recent beginning of the project only results concerning the first sub-objective (identification and classification of the sources of uncertainty) will be presented.