Comparing MLE Vs. NLR in context of Software Reliability Growth Modes (SRGMs)

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Comparing between Maximum Likelihood Estimatorand Non-Linear Regression estimation proceduresfor Software Reliability Growth Modelling

Engineering

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

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 =
1
𝑘
(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

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).

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