1. Hertong Song Department of Computer Science Louisiana Tech University Cluster Reliability Modeling Using UML

2. 2 Reliability Modeling Reliability Modeling Techniques:  Reliability block diagram  Fault trees  Markov chins  Others.

3. 3 System Engineers System engineers, software architects and product managers normally using UML to describe the behaviors of computing systems.

4. 4 A Mapping Tool A tool attempts to map from UML to statistical reliability models Using UML to describe system’s behavior Process the UML output and generate the reliability models Calculate the results

5. 5 Frame Work

6. 6 Gentleware’s Poseidon

7. 7 Output file from UML Once the model is saved, the Poseidon for UML tool generates a zip formatted file named zargo. Inside the zargo there is a XMI file that contains the description for the UML model.

8. 8 Parsing the XML file The failure/repair rates for each node and the relationships between nodes are embedded in this XMI file. These information will then be extracted by parsing the XMI file

9. 9 Markov Chain Model Many intricate system dependencies cannot be adequately represented by none state space modeling methods such as Fault Trees Continuous Markov chains model can be used to handle these kinds of system dependencies

10. 10 Assumptions We assume the nodes are independent to each other, meaning that one node failure does not cause other nodes failure. Once the system is in failure state, the system will not cause more failure.

11. 11 Table 1. UML Tags UML TagsRepresents NameName of the component. Used for grouping failure rateThe failure rate of the component repair rateThe repair rate of the component MinThe minimum components required to keep the system functioning MultiplicityThe number of duplicates of the component

12. 12 An Example for Tag Using

13. 13 Markov Chain Example

14. 14 Algorithm for Constructing MC partition components into distinguished groups. Each tuple represents a group. The number of a tuple represents the number of components in the corresponding group.

15. 15 Algorithm (Continuous) For example, the notation means there are groups; there are identical components in group 1, identical components in group 2 and so on.

16. 16 Algorithm (Continuous) The resulting Markov chain will be in a tree-like structure. The top level (root) of the tree is the initial state of the Markov chain At each level below the root, there are possibilities (braches), for each components in each group may fail

17. 17 Algorithm (Continuous) The tree will propagate with children for each node, until it reaches a leave; which is the minimum number of components required for a certain group to keep the system functioning.

18. 18 Algorithm (Continuous) Once the tree is constructed, each duplicated state will be removed by linking its parent state to the same state in the left part of the tree, with the same failure rate of the removed state.