The production of Official Statistics based on a combination of data from different sources has spread out in recent years and all the National Statistical Institutes (NSIs) are developing new strategies in producing the required outputs. The challenge is to move towards processes where the combination of the available administrative data (AD hereafter) should represent as far as possible the primary source, delivering strong and extensive information about the phenomena under study. Many new experiences have delivered new important results, that can be considered at the basis of the modernization that NSIs are facing. In this view, new processes are taking place and new methodological issues are arising. Among others, a key issue to be considered relates to the development of a new quality framework to assess the quality of Official Statistics based on a multi-source process including AD. This paper focuses on this issue, with the final aim to propose an new evaluation framework, the Total Process Error framework, based on a system of indicators, useful to: (i) help practical decisions about statistical design together with monitoring its development (ii) define quality measure/measures of the new processes and of their statistical outputs.