1. CSE 322: Software Reliability Engineering Topics covered: Architecture-based reliability analysis

2. Failure models of components  Three types of failure models  Probability of failure or reliability:  Constant failure rate:  Time-dependent failure intensity:

3. Steps in architecture-based analysis Architecture-based models Architecture of the application Failure behavior of components Solve the model Superimpose + Performance predictions Performance bottlenecks Reliability predictions Reliability bottlenecks Description Solution

4. Combinations of architecture & failure behavior Absorbing DTMC Probability of failure, R Constant fail. Rate, Time dep. fail int. ( t ) Irreducible DTMC Absorbing CTMC Irreducible CTMC Model #1 Model #2 Model #3 Model #4 Model #7 Model #6 Model #5 Model #8 Model #9 Model #10 Failure behavior of components Architecture Consider only DTMC and CTMC based models Shaded area indicates solution infeasible using DTMC and CTMC models

5. Model #1

6. Example - Model #1 Terminating application 10 modules 1 is the input, 10 is the exit module Architecture modeled by absorbing DTMC Reliability, mean execution time of each component known Probability that the control is transferred to module j, upon execution of module i Reliability of component i Execution time of component i per visit - Time to completion of the application - Reliability of the application 1 234 5 6 789 10

7. Example - Model #1 (contd..) Component 10.9951.00 20.9801.00 30.9901.00 40.9701.00 50.9501.00 60.9951.00 70.9851.00 80.9501.00 90.9751.00 10 0.9851.00 Reliability Mean execution time per visit Known for component i Reliability - 0.8273 Time to completion - 7.7016 units Computed overall

8. Combinations of architecture & failure behavior Absorbing DTMC Probability of failure, R Constant fail. Rate, Time dep. fail int. ( t ) Irreducible DTMC Absorbing CTMC Irreducible CTMC Model #1 Model #2 Model #3 Model #4 Model #7 Model #6 Model #5 Model #8 Model #9 Model #10 Failure behavior of components Architecture Consider only DTMC and CTMC based models Shaded area indicates solution infeasible using DTMC and CTMC models

9. Model #2

10. Example - Model #2,Terminating application, 10 modules 1 is the input, 10 is the exit module Architecture modeled by absorbing DTMC Time independent failure rate known Execution time of the component per visit known Probability that the control is transferred to module j, upon execution of module i Mean execution time of component i per visit Failure rate of component i - Time to completion of the application - Reliability of the application 1 234 5 6 789 10

11. Example - Model #2 (contd..) Component 11.00 2 3 4 5 6 7 8 9 10 1.00 Failure rate Known for component i Expected execution time of the component per visit 0.0010 0.0202 0.0101 0.0305 0.0513 0.0050 0.0151 0.0513 0.0253 0.0151 Reliability - 0.8264 Time to completion - 7.7016 units Computed overall

12. Combinations of architecture & failure behavior Absorbing DTMC Probability of failure, R Constant fail. Rate, Time dep. fail int. ( t ) Irreducible DTMC Absorbing CTMC Irreducible CTMC Model #1 Model #2 Model #3 Model #4 Model #7 Model #6 Model #5 Model #8 Model #9 Model #10 Failure behavior of components Architecture Consider only DTMC and CTMC based models Shaded area indicates solution infeasible using DTMC and CTMC models

13. Model #3

14. Example - Model #3,Terminating application, 10 modules 1 is the input, 10 is the exit module Architecture modeled by absorbing DTMC Time dependent failure rate and mean execution time of each component per visit known Probability that the control is transferred to module j, upon execution of module i Time spent in component i per visit Failure rate of component i - Time to completion of the application - Reliability of the application 1 234 5 6 789 10

15. Example - Model #3 (contd..) Component 11.00 2 3 4 5 6 7 8 9 10 1.00 Failure rate Known for component i Expected total number of faults Mean execution time of the component per visit Fault detection rate per fault Failure rate of the Goel-Okumoto model Reliability - 0.8264 Time to completion - 7.7016 units Computed overall

16. Combinations of architecture & failure behavior Absorbing DTMC Probability of failure, R Constant fail. Rate, Time dep. fail int. ( t ) Irreducible DTMC Absorbing CTMC Irreducible CTMC Model #1 Model #2 Model #3 Model #4 Model #7 Model #6 Model #5 Model #8 Model #9 Model #10 Failure behavior of components Architecture Consider only DTMC and CTMC based models Shaded area indicates solution infeasible using DTMC and CTMC models

17. Model #4

18. Example - Model #4 Non-terminating application 10 modules Architecture modeled by irreducible DTMC Reliability of each component known Probability that the control is transferred to module j, upon execution of module i Reliability of component i - Utilization of module i - Reliability of the application 1 234 5 6 789 10

19. Example - Model #4 (contd..) Component 10.995 0.1073 2 3 4 5 6 7 8 9 10 0.980 0.1055 0.990 0.1091 0.970 0.0765 0.950 0.1714 0.995 0.0459 0.985 0.0823 0.950 0.1129 0.975 0.0549 0.985 0.1341 Utilization of the component Reliability of the application - 0.9753 Computed for component i Computed overall Known for component i Reliability of the component

20. Combinations of architecture & failure behavior Absorbing DTMC Probability of failure, R Constant fail. Rate, Time dep. fail int. ( t ) Irreducible DTMC Absorbing CTMC Irreducible CTMC Model #1 Model #2 Model #3 Model #4 Model #7 Model #6 Model #5 Model #8 Model #9 Model #10 Failure behavior of components Architecture Consider only DTMC and CTMC based models Shaded area indicates solution infeasible using DTMC and CTMC models

21. Model #5

22. Example - Model #6,Terminating application, 10 modules 1 is the input, 10 is the exit module Architecture modeled by absorbing CTMC Reliability of each module known Execution time in each module follows exponential distribution, mean known Probability that the control is transferred to module j, upon execution of module i Mean execution time in component i Reliability of component i - Time to completion of the application - Reliability of the application 1 234 5 6 789 10

23. Example - Model #5 (contd..) Component 10.0010 0.1073 2 3 4 5 6 7 8 9 10 0.0202 0.1055 0.0101 0.1091 0.0305 0.0765 0.0513 0.1714 0.0050 0.0459 0.0151 0.0823 0.0513 0.1129 0.0253 0.0549 0.0151 0.1341 Utilization of the component Computed for component i Computed overall Known for component i Failure rate of the component Failure rate of the application -- 0.0251