Comparing between Maximum Likelihood Estimator

and Non-Linear Regression estimation procedures

for Software Reliability Growth Modelling

Rakesh Rana1, Miroslaw Staron1, Christian Berger1, Jörgen Hansson1,

Martin Nilsson2, Fredrik Törner2

1Computer Science and Engineering, Chalmers/ University of Gothenburg 2Volvo Cars Corporation

Software Reliability Growth Models (SRGMs)

• SRGMs are useful for assessing software reliability (quality), Information is useful for:

– Assessing the release readiness; and

– Testing resource allocation decisions

• Two of the widely known and recommended techniques for parameter estimation are Maximum Likelihood Estimation (MLE) and method of least squares (NLR)

• We compare between the two estimation procedures for their usability and applicability in context of SRGMs

Comparing between MLE & NLR

A better Metrics for measuring Predictive Accuracy

𝑃𝑅𝐸 =𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 − 𝐴𝑐𝑡𝑢𝑎𝑙

𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑

𝐵𝑃𝑅𝐸 =𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 − 𝐴𝑐𝑡𝑢𝑎𝑙

𝜂 ∗ 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 + (1 − 𝜂) 2 ∗ 𝐴𝑐𝑡𝑢𝑎 − 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑,

𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒊𝒐𝒏 𝑨𝒄𝒄𝒖𝒓𝒂𝒄𝒚:

𝑤ℎ𝑒𝑟𝑒 𝜂 = 1 𝑖𝑓 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑>𝐴𝑐𝑡𝑢𝑎𝑙

0 𝑖𝑓 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑<𝐴𝑐𝑡𝑢𝑎𝑙

𝑀𝑆𝐸 = 1𝑘(𝑎𝑖 − 𝑝𝑖)

2

𝑘 − 𝑞

𝑮𝒐𝒐𝒅𝒏𝒆𝒔𝒔 − 𝒐𝒇 − 𝒇𝒊𝒕:

*PRE provides asymmetric value based on over or under prediction.

Thus we define Balanced Predictive Relative Error, BPRE

Comparing Parameters using MLE & NLR

Table: Comparing parameters with different estimators

Comparing between MLE & NLR

Comparing between MLE & NLR

Thank You

The research presented here is done under the VISEE project which is funded by Vinnova and Volvo Cars jointly under the FFI programme (VISEE, Project No: DIARIENR: 2011-04438).