1. A User-Oriented Software Reliability Model Per Trygve Myhrer 20 februar 2004 1980 Roger C. Cheung

2. Overview Intro to Markov model Software reliability Model for Software Reliability Model of a program Reliability of system Use of the model Conclusion 2

3. Markov model System states, seen as nodes Probabilities of transitions Conditions for a Markov model: Probabilities are constants No memory of paste states N1N1 N2N2 N3N3 N4N4 P 12 P 13 P 14 P 34 P 24 P 31 P 41 Transition matrix To Node N1N1 N2N2 N3N3 N4N4 From Node N1N1 P 11 P 12 P 13 P 14 N2N2 P 21 P 22 0P 24 N3N3 P 31 0P 33 P 34 N4N4 P 41 00 P 44 P 21 3

4. Software reliability 1 Difficult to give a formal definition on “software reliability” One if correct, and zero if incorrect Counting bugs in a program –Not interesting for user Failure: If output are incorrect or indefinitely delayed 4

5. Software reliability 2 Reliability: probability that a program gives correct output with a typical set of input data from user environment Reliability depends on user profile Nonexecuted code have no influence on output Little used modules might be less important for reliability of the system 5

6. Module A module is defined to perform a particular function Reliability of a module: –Probability that the module performs the function correctly A module passes result to next module A module is logical independent –For design, programming and testing 6

7. Model for Software Reliability Program runs correct only if the correct sequence of modules are executed and every module executed gives the correct result The reliability of the modules are independent. –The probability of a module executed correct are depended on the present module only and is independent of the past history Model is a graph with Markov behaviour –Probabilities are constants –No memory of paste states 7

8. Model of a program 1 The program is seen as a graph Assumes there is one entry node and one exit node Every transition from node N i to node N j has a probability of P ij –If no connection between N i and N j, then P ij = 0 N1N1 N2N2 N3N3 N4N4 P 12 P 13 P 14 P 34 P 24 P 31 P 21 Output Input 8

9. Model of a program 2 Adds R i, that is the reliability of a module Two new exit states are added –C program return correct output –F if any module have a fault, the program do not return correct output New transitions N1N1 N2N2 N3N3 N4N4 R 1 P 12 R 1 P 13 R 1 P 14 R 3 P 34 R 2 P 24 R 3 P 31 R 2 P 21 F C 1-R 1 1-R 2 1-R 3 1-R 4 R4R4 9

10. Reliability of system 1 Transition matrix of the system, P P To Node CFN1N1 N2N2 N3N3 N4N4 From Node C100000 F010000 N1N1 01-R 1 0R 1 P 12 R 1 P 13 R 1 P 14 N2N2 01-R 2 R 2 P 21 00R 2 P 24 N3N3 01-R 3 R 3 P 31 00R 3 P 34 N4N4 R4R4 1-R 4 000 0 10

11. Reliability of system 2 P n (i,j) – probability that the system goes from the starting state i, and that the system enters the absorbing states j  {C,F} at or before the nth step The reliability of the system is the probability that it gets to state C, when starting at node,N 1 and n →∞ R = P n (N 1,C) 11

12. Use of the model Measure reliability Possible to measure for what modules increasing reliability will affect reliability of the system most Can use a more effective testing strategy Critical modules that have been shown to be reliable should be avoided changing Not all bugs are equally costly 12

13. Conclusion The article follows IMRAD Research methods –Look into what exists of models –Made a mathematic model –Test on a small experiment 13

14. Questions ?