A User-Oriented Software Reliability Model

Per Trygve Myhrer 20 februar 2004

1980Roger C. Cheung

Overview

• Intro to Markov model

• Software reliability • Model for Software Reliability• Model of a program• Reliability of system

• Use of the model• Conclusion

2

Markov model

• System states, seen as nodes

• Probabilities of transitions

Conditions for a Markov model:

• Probabilities are constants

• No memory of paste states

N1 N2

N3N4

P12

P13

P14

P34

P24P31

P41

Transition matrixTo Node

N1 N2 N3 N4

From Node

N1 P11 P12 P13 P14

N2 P21 P22 0 P24

N3 P31 0 P33 P34

N4 P41 0 0 P44

P21

3

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

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

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

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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

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 Ni to node Nj has a probability of Pij

– If no connection between Ni and Nj, then Pij= 0N1 N2

N3N4

P12

P13

P14

P34

P24P31

P21

Output

Input

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Model of a program 2

• Adds Ri, 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 N1 N2

N3N4

R1P12

R1P13

R1P14

R3P34

R2P24R3P31

R2P21

F

C

1-R1

1-R2

1-R3

1-R4

R49

Reliability of system 1

• Transition matrix of the system, P

PTo Node

C F N1 N2 N3 N4

From Node

C 1 0 0 0 0 0

F 0 1 0 0 0 0

N1 0 1-R1 0 R1P12 R1P13 R1P14

N2 0 1-R2 R2P21 0 0 R2P24

N3 0 1-R3 R3P31 0 0 R3P34

N4 R4 1-R4 0 0 0 0

10

Reliability of system 2

• Pn(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,N1 and n →∞

• R = Pn(N1,C)

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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

Conclusion

• The article follows IMRAD

• Research methods– Look into what exists of models– Made a mathematic model– Test on a small experiment

13

Questions ?