  Context: Tertiary studies are becoming increasingly popular in software
engineering as an instrument to synthesise evidence on a research topic in a
systematic way. In order to understand and contextualize their findings, it is
important to assess the quality of the selected secondary studies. Objective:
This paper aims to provide a state of the art on the assessment of secondary
studies' quality as conducted in tertiary studies in the area of software
engineering, reporting the frameworks used as instruments, the facets examined
in these frameworks, and the purposes of the quality assessment. Method: We
designed this study as a systematic mapping responding to four research
questions derived from the objective above. We applied a rigorous search
protocol over the Scopus digital library, resulting in 47 papers after
application of inclusion and exclusion criteria. The extracted data was
synthesised using content analysis. Results: A majority of tertiary studies
perform quality assessment. It is not often used for excluding studies, but to
support some kind of investigation. The DARE quality assessment framework is
the most frequently used, with customizations in some cases to cover missing
facets. We outline the first steps towards building a new framework to address
the shortcomings identified. Conclusion: This paper is a step forward
establishing a foundation for researchers in two different ways. As authors of
tertiary studies, understanding the different possibilities in which they can
perform quality assessment of secondary studies. As readers, having an
instrument to understand the methodological rigor upon which tertiary studies
may claim their findings.
