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COTS (commercial-off-the-shelf) software products are usually provided in a packaged style without the source code but with many ready-to-use functions. Generally, their vendors are reluctant to disclose the source code. Thus, the major way of quality evaluation and certification requires dynamic behavior testing, essentially black-box testing. Since observing every aspect of external software behavior is almost impossible, it is crucial to designate an adequate range for quality evaluation such as an adequate number of quality checklists or product quality metrics for external behavior testing. Hence, to establish rules of selecting quality evaluation criteria in systematic ways, there have been attempts to analyze and utilize the past records of software evaluation. In this paper, multiple characteristics of software are mapped as nodes to affect and determine the priority ranks of external software quality metrics on Bayesian belief network. The nodes are set to be under the influence of multiple inheritances so that every external characteristic of COTS software is considered thoroughly.