This document contains the slides from a presentation given by Dr. Thomas Fehlmann on October 7, 2015 in Kraków, Poland. The presentation discusses using transfer functions and the solution profile to combine multiple functional size measurement methods into a single measurement in accordance with international standards for measurement. This allows defining a functional size unit specific to the transfer function and measurement goals. The solution profile shows the contribution of each size count to measurement precision and goals.

1. Session 5 in Kraków, October 7, 2015
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 1

2. Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 2
1981: Dr. Math. ETHZ
1982-89: Manager Software–Development
1990-95: Senior Consultant – Digital Equipment Corp.
1996-99: Sales Support Manager – Proposal Center
1999ff: Euro Project Office AG, Zürich
Akao Price 2001 for original contributions to QFD
Member of the Board of QFD Institute Germany – QFD Architect
Chair of SwiSMA, the Swiss Software Metrics Association
2000ff: Six Sigma Black Belt for GMC Software AG
Lean Six Sigma for Software Development
Quality Function Deployment (QFD) and New Lanchester Theory
Net Promoter Score Associate
2012: Member of the DASMA Board
2013: Vice-President ISBSG

3. Eberhard Kranich studied Mathematics and Computer Science, with an emphasis on
Mathematical Statistics, Mathematical Optimization, and on Theory of Polynomial
Complexity of Algorithms. He worked at T-Systems International GmbH in Bonn until
2013, Germany, as a Six Sigma Black Belt and Quality Assurance Manager, mainly in
the context of software development.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 3

4. In fact, this is an open end talk. Currently, we only present project costing based on
measurements; the software security and system safety measurements are yet to
come…
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 4

5. The Bureau International des Poids et Mesures originates from the Metre Convention
of 20 May 1875, that introduced the metrics system is almost all countries in the
world (yes, including the USA and the UK).
Dr. Thomas Fehlmann October 7, 2015
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6. Both documents are now available as ISO documents, although not completely
conformant to the technical standard format used with ISO/IEC, therefore publishes
as “guides”:
• The VIM: ISO/IEC Guide 99:2007 - International vocabulary of metrology – Basic
and general concepts and associated terms
• The GUM: ISO/IEC CD Guide 98-3, 2015 - Evaluation of measurement data – Part 3:
Guide to uncertainty in measurement (GUM)
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 6

7. Measurable entities that are physical are the most simple to measure. However,
some physical entities change behavior under measurement (quantum effects), and if
you try measuring anything involving humans they adapt behavior to the
measurement goal. Then, measurement rather becomes a management science.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 7

8. The IFPUG counting method violates the VIM in many respects
• There is no zero on the 𝐼𝐹𝑃 scale
• There is no one on the 𝐼𝐹𝑃 scale – not even Peano axioms hold
• Changing complexity from “Low” to “Medium” to “High” might cause goat jumps
• If everything is “High” in complexity, the count is capped
• Counts are not additive – 𝐼𝐹𝑃 𝐴 + 𝐼𝐹𝑃 𝐵 ≠ 𝐼𝐹𝑃 𝐴 + 𝐵
Some other counting methods (COSMIC) are at least not violating the VIM.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 8

9. A model allows exact, digital counts of the model elements. The question is whether
the model is accurately representing the software under scrutiny. Thus, measurement
accuracy based on counting model elements refers to the model validity in view of
the measurement goals and not to the counting rules. Abran uses the term Validation
of the model against Verification of the measurement context to discuss measure-
ment accuracy (Abran, Software Metrics and Software Metrology, 2010, p. 34).
Counts are something else than measurements.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 9

10. What is the single most important invention of the 20th century?
The proof that the Fast Fourier Transfer (FFT) is not NP-complete made the deepest
impact on humankind probably since invention of cooking by a fire (Cooley & Tukey,
1964). It led to the possibility of transferring audio signals in predictable time into
digital code. Previously, sounds were analogous oscillations of the atmosphere, or of
electro-magnetic potentials, caused by beings or loudspeakers. The FFT did allow
describing with digital numbers what the original oscillations where. Thus, it became
possible to build chips that transformed audio signals into storable digital code and
later video signals as well. All the music and entertainment stuff that today makes up
for a trillion-euro industry started with that invention. Today it populates computers,
laptops, phones and television sets connecting by a global internet.
The FFT did not come by coincidence; it was the result of long years of solid research
in pure mathematics, especially in linear algebra. FFT transforms audio signals
captured by a microphone as electrical pulses into digital numbers. To be more
precise, the FFT algorithm selects the Fourier base functions in the functional vector
space that model the analogous signal and represents the signal by the coordinates
of the unit vector in this space. This works like a linear vector space; however, the
base units are functions, not points in space. Finding controls for a transfer function
to explain the observed response is quite similar.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 10

11. The calculation of the Eigenvector is mathematically simple; nevertheless, this is a
relatively new invention (Gauss, as always…), however, the old Greeks didn’t seem to
know this optimization method (or we lost all references during the middle ages).
Basically, the idea is to revert cause and effect. Mathematically, this is simple; if you
try this for the physical world, it won’t work because time runs forward.
All you have to do is transpose the transfer function matrix, and calculate the
combined symmetrical square matrix 𝑨𝑨⊺
. Such matrices, if positive definite, have a
principal Eigenvector (theorem of Perron).
Using that Eigenvector, the solution𝒙 = 𝑨⊺
𝒚 𝐸 is simple to calculate.
For Freaks: Multiply 𝑨 by 𝑨⊺
The transposed dual matrix 𝑨⊺
Row by row
𝑨𝑨⊺
𝑖,𝑗 =
𝑘=1..𝑚
𝑎𝑖,𝑘 𝑎 𝑘,𝑗
Result: quadratic 𝑚 𝑥 𝑚 Matrix
Now 𝑨𝑨⊺
has Principal Eigenvector 𝒚 𝐸
𝑨𝑨⊺
𝒚 𝐸 = 𝒚 𝐸 ≅ 𝒚
𝒙 = 𝑨⊺
𝒚 𝐸 solves 𝑨𝒙 = 𝒚 𝐸, thus approximately 𝑨𝒙 ≅ 𝒚
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 11

12. Assume there is some “oracle” denoted as 𝑨⊺
𝒚 guessing a profile 𝒙 𝑬 = 𝑨⊺
𝒚 for any
chosen set of controls. Chapter 2: Transfer Functions will explain how to construct
such oracles. This oracle 𝒙 𝑬 = 𝑨⊺
𝒚 predicts the control profile 𝒙 𝑬 = 𝑥1, 𝑥2, … , 𝑥 𝑛 ,
enabling users to select and prioritize controls, such that they can start with the most
important first and fine-tune with the least expensive ones. This is what traditionally
QFD aims for – however, the methods used for finding such a profile for 𝒙 𝑬 are often
relying more on experienced moderators than on mathematical reasoning and
evidence.
If the oracle 𝑨⊺
𝒚 is not perfect, as happens for oracles from time to time, the
convergence gap tells the difference. If the oracle is perfect, then the process
becomes lean.
Thus, if such an oracle exists for the transfer function 𝑨, the selected controls are
capable of delivering a process response 𝒚 𝑬 = 𝑨𝒙 𝑬 close enough to the desired
response 𝒚. If the goal profile 𝒚 and achieved response 𝒚 𝑬 = 𝑨𝒙 𝑬 are close enough,
the process repeats without variation. Consequently, the convergence gap is an
indicator similar to the standard deviation sigma for the degree of variation that a
process executes during one loop.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 12

13. Every of the major functional sizing methods states as the first tasks in counting:
define what the measurement goal is. However, none of the methods specifies how
to measure the distance between goal target and achieved target. This simply is left
to qualitative considerations.
In contrary, when playing football, teams assess with scrutiny why they hit or missed
the goal target. So, let’s learn from soccer teams!
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 13

14. As an example, assume the measurement goal is to predict project cost. It is
understood that both functionality and quality add to cost; the goal profile had been
defined based on previous experiences of the project team.
Also, the organization adds cost, depending upon public exposure and stakeholders.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 14

15. Since this is serious, the team uses several counting methods to identify the controls
for project costing. Two ISO standards; one for non-functional size based on the
Buglione-Trudel matrix, since it is agile development, or SNAP, if more traditional
approaches apply.
Legal size is a count based on the applicable legal laws & regulations; something
often ignored by technically oriented people.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 15

16. The transfer function maps the estimation controls on the measurement goal profile.
In this case, the impact measurements in the QFD matrix cells are expert judgments
obtained in the QFD way. The solution profile for counts indicates how much weight
each count has concerning the measurement goals. In this case, it refers to the
consolidated cost estimation for the whole project. Thus, transfer functions make
functional size counts compliant to metrology standards. The convergence gap
reflects measurement precision with regard to the chosen measurement goals.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 16

17. The solution profile shows the overall importance, or contribution, that each of the
counts adds to the measurement goals. Thus, measurement precision is not with
regard to the count but with regard to the measurement goals; in accordance with
the standards for measurement imposed by the Bureau International des Poids et
Mesures, the VIM (ISO/IEC Guide 99:2007, 2007) and the GUM (ISO/IEC CD Guide 98-
3, 2015). The solution profile combines several functional sizing methods into one
measurement; thus, it becomes possible to define a functional sizing unit per transfer
function. The counts contribute to measurement precision in specific ways.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 17

18. Understanding measurements as transfer function is also a big step forward for the
VIM and the GUM into the 21st century. For software metrics, it opens the path
towards more measurements based on counts and sometimes also assessments.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 18

19. The authors have published quite a bit on the subject – e.g., in QFD symposia, at SW
metrics conferences like MetriKon or IWSM / Mensura; also at Lean Six Sigma
Conference Glasgow, Strathclyde and in Zurich.
There is a book in in progress for print: "Managing Complexity“. A preprint is available
from the authors.
Dr. Thomas Fehlmann October 7, 2015
© Euro Project Office AG, 2015 Page 19