**Semantic interoperability in the OR.NET project on networking of medical devices and information systems A requirements analysis**

For a fault we keep those detections tests that when using give the higher values, in set . Moreover, for the same fault we keep those detections that when using give the higher value, in set Theorem For some fault , the set of tests is identical to the set of tests . Proof: Set contains the tests that give the maximum values when calculating for fault . Semantic interoperability in the OR.NET project on networking of medical devices and information systems A requirements analysis By substituting we have However, the term is constant since it does not depend on and, thus The tests to be included in test set are selected by obtaining times the times Since all are non-negative integers the same test is obtained By Semantic interoperability in the OR.

NET project on networking of medical devices and information systems A requirements analysis Set contains the tests which are elements of that give the maximum value in we have illustrating the concepts used in Theorem. Again, the term does not depend on , so we get The set of tests that give the maximum reduction in specified bits can be obtained by Since all are non-negative integers we get Equation implies that the set contains the tests from that have the minimum , the tests that are elements of the subset of of size that has the minimum sum of . The subset of of size that has the minimum sum ofis given in which, Semantic interoperability in the OR.NET project on networking of medical devices and information systems A requirements analysis however, gives the set .

## Semantic interoperability in the OR.NET project on networking of medical devices and information systems A requirements analysi

Semantic interoperability in the OR.NET project on networking of medical devices and information systems A requirements analysis Hence, sets and are identical. Theorem suggests that using for selecting the best tests to detect each fault gives exactly the same result as using Thus, there is no need to find the contribution in specified bits for all combinations of tests in the set for some fault , in order to keep those tests that give the highest reduction in terms of specified bits. presents an indicative example that illustrates the rationale of Theorem and lists all the necessary calculations. The diagram on the left shows a test Semantic interoperability in the OR.NET project on networking of medical devices and information systems A requirements analysis set and a subset that includes all the four tests that cover fault , and . The number above each test indicates the number of specified bits that can become don’t cares if and only is no longer detected by the test For instance, bits of can become don’t cares and this relaxation does not affect any other fault detection of , except that of .

Now, assume that and according to the problem examined we have to select that subset of with cardinality that will give me the largest gain in specified bits, defined above as . This requires the calculation of for all six pairs of tests in and select the maximum These calculations are done using and are listed on the right table For instance, if tests and are selected to detect , bits can be converted to don’t cares. Obviously, these calculations will lead to selecting the set of tests as , since this gives the largest relaxing benefit. n/d here means that the corresponding combination will reduce the -detect fault coverage of the test and it should not be considered as a possible solution.