Evaluation of standard reliability growth models in

the context of automotive software systems

SRGMs: Software Reliability

Growth Models

Rakesh Rana1, Miroslaw Staron1, Niklas Mellegård1, Christian Berger1,

Jörgen Hansson1, Martin Nilsson2, Fredrik Törner2

1Software Engineering division,

Department of Computer Science and Engineering,

Chalmers/ University of Gothenburg 2Volvo Cars Corporation

This Car Runs on Code

“It takes dozens of mircroprocessors running 100 million lines of

code to get a premium car out of the driveway, and this software is

only going to get more complex” -ieee spectrumRef: http://spectrum.ieee.org/green-tech/advanced-cars/this-car-runs-on-code

Reliability

*Reliability and dependability are very important features

of any computer system.

*Have we done enough testing?

*Is the software ready for release?

*How should we adjust/optimize our testing strategy?

SRGM -> Software Reliability and Maturity

SRGM -> Use for Automotive Software Projects

Data used (Automotive Project)

Mellegård, N., Staron, M., and Törner, F.: ‘A light-weight defect classification scheme for embedded

automotive software and its initial evaluation’

Different Software Reliability Growth Models

Model Name Model Type Mean Value Function Reference

Models with 2 parameters

Goel-Okumoto (GO) Concave 𝑚 𝑡 = 𝑎(1 − 𝑒−𝑏𝑡 ) [11]

Delayed S-shaped model S-shaped 𝑚 𝑡 = 𝑎(1 − (1 + 𝑏𝑡)𝑒−𝑏𝑡 ) [12]

Rayleigh model 𝑚 𝑡 = 𝑎𝑒−𝑏/𝑡

Models with 3 parameters

Inflection S-shaped model S-shaped 𝑚 𝑡 =

𝑎(1 − 𝑒−𝑏𝑡 )

(1 + 𝛽𝑒−𝑏𝑡 )

[9]

Yamada exponential imperfect

debugging model (Y-ExpI)

S-shaped 𝑚 𝑡 =

𝑎𝑏

∝ + 𝑏 (𝑒∝𝑡 − 𝑒−𝑏𝑡 )

[13]

Yamada linear imperfect

debugging model (Y-LinI)

S-shaped 𝑚 𝑡 = 𝑎 1 − 𝑒−𝑏𝑡 1 − ∝

𝑏 + ∝ 𝑎𝑡 [13]

Logistic population model S-shaped 𝑚 𝑡 = 𝑎

1 + 𝑒−𝑏 𝑡−𝑐 [14]

Gompertz model S-shaped 𝑚 𝑡 = 𝑎𝑒−𝑏𝑒−𝑐𝑡

[15]

Two parameter models

Three parameter models

Evaluating model fits using MSE

Evaluating model fits using MSE

Evaluating models on Asymptote

Evaluating models on Asymptote

Conclusions and further work

*Two parameters models: fit - reasonable, asymptotes -

unrealistic;

*Logistic and inflectionS: Best fit to our data among the

different models tried;

*Important factors: Using appropriate time scale.;

*Using parameter estimates from two parameter models

and current project information, can give useful insight for

optimizing the resource allocation going forward.

Summary and Impact

*Logistic and inflectionS and Gompertz model gives best

fit and asymptote predictions.

*Identifying right models and using SRGMs in the

company and automotive sector in general will:-

*Help assess the reliability of software developed and thus the

release readiness.

*Using SRGM during the project can help test and quality

managers to make optimal testing resource allocation decisions.

*Thus correct use of SRGMs help the company & the automotive

industry to develop and release high quality software.

Thank You