This paper presents formalizations that capture definitions of a number of concepts of the ISO/IEC 15504-5 process assessment model and the CMMI v1.3 constellations process models and relations among the concepts. The formalizations are expressed in a formal language, OWL. The main objectives for these formalizations are to be consistent with the ISO/IEC 15504-5 process assessment model and the CMMI-DEV/SVC/ACQ v1.3 models and to be effective, i.e., to allow for an automatic determination of an organizations maturity level and of a process capability level based upon data collected during an assessment. The formalizations are presented in a number of levels, from more general concepts to more specific. To assess the validity of the ISO/IEC 15504-5 formalization, a number of test cases for the scenario of automatic determination of the capability levels were developed. To assess the validity of the CMMI v1.3 formalizations, a number of real cases were selected from the CMMI institute published appraisal results with the purpose of validating the automatic determination of both organizational maturity and process areas capability levels. A set of OWL reasoners were then used to derive the capability levels for a specific process group (regarding the ISO/IEC 15504-5) and to derive the organizational maturity and process areas capability levels for the CMMI-DEV v1.3 constellation. While the test results were all positive, the real value of these formalizations comes from the fact that they faithfully captured the main aspects of ISO/IEC 15504-5 and CMMI v1.3, both well established and accepted models for the assessment of organizational processes, and that an inference engine was able to support the assessment of processes capability levels and of organizations maturity levels.
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