A Proposal of Derivation Methods of FP Transformation Formulas
Masateru Tsunoda, Shinsuke Matsumoto, Akito Monden, Ken-ichi Matsumoto
Graduate School of Information Science, Nara Institute of Science and Technology{masate-t, shinsuke-m, akito-m, matumoto}@is.naist.jp

Abstract

thods is the same and some metrics are able to be used
for multiple regression models.

When FP measurement methods are different between the same functional size projects, FPs are different between them. FP measurement methods areoften customized by software vendors. To reinforce
accountability for a customer, FP based on a customized method should be transformed to FP based on astandard method. So we proposed two derivation methods of FP transformation formulas. One method isfocused on productivity. Productivity of each FP measurement method is transformed by Z-score to derive
FP transformation formulas. The other method builds
a multiple linear regression model whose objective
variable is FP and one of the explanatory variables iseffort for each FP measurement method, and makes
simultaneous linear equations by the models to derive
FP transformation formulas.

2. Derivation Method Based on Productivity

Function point (FP) denotes software functionalsize, and there are many FP measurement methods
such as IFPUG, NESMA, and COSMIC-FFP. Moreover, FP measurement methods are often customized bysoftware vendors. When FP measurement methods aredifferent between the same functional size projects,
FPs are different between them. To reinforce accountability for a customer, FP based on a customized method should be transformed to FP based on a standard
method. Additionally, projects can be compared precisely with a benchmarking dataset like ISBSG withtransforming FP. So we propose two derivation methods of FP transformation formulas. One method isfocused on productivity. This method is used when
productivity of projects where FPs are measured bydifferent methods seems the to be same. The othermethod uses a multiple linear regression model. Thismethod is used when it is not obvious that productivityof projects where FPs are measured by different me-Step1. Deriving a productivity transformation formula
We derive a productivity transformation formulawith Z-score, considering average and variance. μA
indicates average of productivity of projects in whichFPs were measured by method A, and σA indicatesstandard deviation. μB indicates average of productivity of projects in which FPs were measured by the method B, and σB indicates standard deviation. PAi indicates productivity of Proji (i = 1, 2, …, n) in which FP
was measured by method A. That is, PAi is calculatedwith FP measured by method A. PˆBi is converted prod***********ooooooooooooooo0.80

Productivity

1. Introduction

We assume that the difference of FP measurement
methods causes the difference of productivity. Productivity is defined as Effort/FP. Figure 1 shows productivity of projects whose FPs are measured by different
FP measurement methods. In this method, we alignproductivity of each FP measurement method and derive FP transformation formulas as follows.

0.60
0.40

**o0.20
0.00
COSMIC-FFPIFPUGNESMA

Fig.1 Example of productivity of each FP measurement method

uctivity of Proji , assuming FP was measured by method B in the Proji . Namely, PˆBi is assumed to be calculated with FP measured by method B. PAi is converted to PˆBi with the following formula based on Zscore.

PˆBi  B ( P Ai   A )   B(1)
A
Step 2. Calculating converted FP value of eachprojectFAi indicates FP of Proji (FAi is measured by method A), Ei indicates development effort of Proji , andFˆBi indicates FP of Proji , assuming FP is measured bymethod B in Proji . FˆBi is expressed as FˆBi  PˆBi Ei because Pˆ  FˆBi . With formula (1) and P  FAi ,AiBiEiEiFˆBi  PˆBi Ei is transformed as the following formula.

FˆBi  B FAi  ( B  A  B ) Ei(2)AEach FˆBi of Proji is calculated, using formula (2).

A

Step 3. Deriving an FP transformation formula
Pairing FAi with FˆBi , a simple linear regression
model is built. The objective variable is FP measured
by method B, and the explanatory variable is FP
measured by method A. This model changes over fromFP measured by method A to FP measured by method
B.
In addition to FP measurement methods, some factors affect productivity of software projects [1][2]. To
weaken the affect of other factors, projects should be
stratified before deriving FP transformation formulas.
For example, if team size and programming language
have a strong relationship to productivity, only
projects that have almost the same team size and same
programming language are used for deriving FP transformation formulas.

3. Derivation Method Based on Multiple
Linear Regression Models
In this method, a multiple linear regression model
whose objective variable is FP and one of the explanatory variables is effort is built for each FP measurement method, and simultaneous linear equations are
made by the models to derive FP transformation formulas. Using metrics as explanatory variables of themultiple linear regression model, influence of othermetrics can be eliminated.
On a project, FAi denotes FP measured by method A,FBi denotes FP measured by method B, Ei denotes de-velopment effort, and Xi1, Xi2, …, Xij (i = 1, 2, …, n，j= 1, 2, …, m) denote metrics except for FP and effort.
The relationship of FAi and Ei (the model whose objective value is FP measured by method A) is denoted as
the following formula with function fA.
FAi = fA(Ei , Xi1, Xi2, …, Xij)

(3)

Similarly, the relationship of FBi and Ei (the model
whose objective value is FP measured by method B) is
denoted as the following formula using function fB.
FBi = fB(Ei , Xi1, Xi2, …, Xij)

(4)

When simultaneous linear equations are made byformulas (3) and (4), values of FAi , Xi1, Xi2, …, Xij are
given, and unknowns are Ei and FBi , the unknown FBi(and Ei ) can be decided because the number of unknowns and the number of equations are the same.
The formula that changes over from FP measured bymethod A to FP measured by method B is set up bysolving FBi with formulas (3) and (4).
FBi = f ’(FAi , Xi1, Xi2, ..., Xij)

(5)

4. Conclusions
We proposed two derivation methods of FP transformation formulas, which are based on the differenceof productivity and on multiple linear regression models. Our future works are applying the proposed method to the actual project dataset, deriving FP transformation formulas, and confirming validity of theformulas by measuring errors when FPs are transformed from method A to B, and the transformed FPs
are transformed from B to A again.

Acknowledgements
This work is being conducted as a part of the StagE
Project, the Development of Next Generation IT Infrastructure, supported by the Ministry of Education, Culture, Sports, Science and Technology.]

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