Journal of Software Engineering and Applications, 2012, 5, 797-809 Published Online October 2012 (
Software Measurement Methods: An Analysis of Two
Jean-Marc Desharnais, Alain Abran
Department of Software Engineering and IT, École de Technologie Supérieure, Montreal, Canada.
Received August 22nd, 2012; revised September 24th, 2012; accepted October 6th, 2012
In software engineering, software measures are often proposed without precise identification of the measurable concepts
they attempt to quantify: consequently, the numbers obtained are challenging to reproduce in different measurement
contexts and to interpret, either as base measures or in combination as derived measures. The lack of consistency when
using base measures in data collection can affect both data preparation and data analysis. This paper analyzes the simi-
larities and differences across three different views of measurement methods (ISO International Vocabulary on Metro-
logy, ISO 15939, and ISO 25021), and uses a process proposed for the design of software measurement methods to
analyze two examples of such methods selected from the literature.
Keywords: Software Measures; Base Measures; Derived Measures; Measurement Method; Attributes; Software
Quality Model; Metrology; Software Metrics
1. Introduction
In the sciences and in engineering, the consensus on rigo-
rous measurement definitions and base quantities is well
established. For instance, the ISO 2007 edition on me-
trology, the International Vocabulary of Metrology—Basic
and General Concepts and Associated Terms [1], pre-
sents 144 measurement terms in five categories and in
increasing order of complexity (in parentheses, the num-
ber of terms in each category) [2]:
Quantities and Units (30 terms);
Measurements (53 terms);
Devices for measurement (12 terms);
Properties of measuring devices (31 terms), and
Measurement Standards - Etalons (18 terms).
In the International System (SI) of units, there are 7
base quantities (length, mass, temperature, luminous in-
tensity, time, etc.), from which all other quantities in the
sciences and in engineering are derived. Of these 7 base
quantities, only time (and multiples of its base unit, the
second) is used in software engineering for the mea-
surement of two project parameters: duration and effort.
These parameters are then used in derived quantities,
such as number of faults and number of tests, to represent
some aspects of software quality, such as availability and
In the field of software engineering, and in ISO 9126
parts 1, 2, 3 and 4 [3-6], the single term metrics is often
used in reference to multiple concepts: for example, the
quantity to be measured (measurand1), the measurement
procedure, the measurement results or models of rela-
tionships across multiple measures, and measurement of
the objects themselves. In the software engineering lite-
rature, the term was, until recently, applied to:
Measurement of a concept: e.g. cyclomatic complex-
ity [2, ch. 7] [7];
Quality models: e.g. ISO 9126—software product
quality [3-6];
Estimation models: e.g. Halstead’s effort equation [2,
ch. 6] [8], Use Case Points—[2, ch. 9], COCOMO 1
and II, Boehm [9,10];
Cohesion and coupling [11-13].
In recent decades, hundreds of so-called software metrics
have been proposed by researchers and practitioners alike,
in both theoretical and empirical studies, for measuring
software products and software processes [6-9]: most of
these metrics were designed based either on intuition on
the part of researchers, or on an empirical basis, or both,
and they are often characterized by the ease with which
some development process entities can be counted. The
inventory of software metrics is at the present time so
diversified and includes so many individual proposals
that it is not seen as economically feasible for either the
industry or the research community to investigate each of
1A measurand is defined as a particular quantity subject to measurement
the specification of a measurand may require statements about quanti-
ties such as time, temperature, and pressure [1].
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Software Measurement Methods: An Analysis of Two Designs
the hundreds of alternatives proposed to date.
With the notable exception of the measurement of the
functional size of software (ISO 19761 [14], ISO 14143
[15], etc.), no base measure for software has yet reached
an international level of standardization. Initiatives to
precisely define and develop international consensus on
base measures for software and software quality are few
and far between. For instance, there are still some no-
ticeable differences in the vocabulary used for software
measurement process in ISO 15939 [16] and ISO 9126
[3-6], compared with the measurement vocabulary adopted in
the sciences and in engineering as a common taxonomy
of measurement terms, including metrological terms like
meter, lumen, degree Celsius, etc. [1].
The ISO 9126 quality model (and its successor, the
ISO 25000 series [17], currently in preparation) for soft-
ware products is well known among researchers and
practitioners [18]. This quality model includes a submodel
shared by the internal and external views of the quality of
the software product, and a separate submodel for the
quality-in-use of a software product. These two submodels
include 10 quality characteristics, 27 subcharacteristics,
and an inventory of over 250 derived measures proposed
to quantify attributes of these quality characteristics and
A number of measurement-related weaknesses have
been identified in ISO 9126, such as the following:
- There is no single list of base measures in ISO 9126:
they are spread throughout the descriptions of the
250+ so-called metrics, which, according to the VIM,
should be referred to as derived measures, that is: a
combination of base measures [18].
- In [18], it was pointed out that these 250+ derived
measures are based on what appears to be 80 distinct
base measures [18].
- These 80 base measures lack a detailed description of
the base quantities, the base units, and the attributes
they are attempting to quantify. For some base measures
in ISO 9126, in fact, it is difficult to figure out exactly
what a measurable concept is, as it is variously and
ambiguously referred to (as: a function, a question-
naire, an item, a cost, an installation step, an opera-
tion, etc.), which means that its definition is very
much open to interpretation [18]. This problem in not
unique to ISO 9126: in software engineering, the at-
tributes to be measured are not often defined system-
atically, as can be observed in ISO 24765—Vocabulary
for systems and software engineers [19]: the term er-
ror, for instance, has 4 definitions, defect has 3 defi-
nitions, failure has 2 definitions, fault has 3 defini-
tions, etc. Also, the definition of the attribute to be
measured in [18] is only part of one of the necessary
steps in the design of the measurement method for
any attribute. For instance, no corresponding measure-
ment method has been proposed for the base meas-
ures introduced in ISO 9126, nor is there any indica-
tion of what the measurement units might be.
- The numerical rules for some of the proposed metrics
are poorly defined, and include improper mixes of
scale types [2, p. 220].
This ISO 9126 series is currently under revision by an
ISO working group (ISO/IEC JTC1/SC7 WG6), and one
of the challenges to improving its measurement results is
to strengthen its foundations, including the set of base
measures that are spread throughout Parts 2 - 4 of the series
On the basis of the existing literature, this paper ana-
lyzes the similarities and differences across three different
views of measurement methods (ISO International Vo-
cabulary on Metrology, ISO 15939, and ISO 25021).
Comparing measurement views from these standards
will allow researchers to carry out comparative studies of
multiple alternative measures for the same attributes, and
then to publish their studies and recommendations, so
that industry has the necessary information on which to
base their selection of a measurement method appropriate
to their needs. We have no intention of proposing a spe-
cific software measurement framework in this paper, even
though it would be desirable to do so, but instead we aim
to provide a better understanding of two measurement
methods, in order to help software engineers obtain ac-
curate, repeatable, and reproducible measurement results.
This paper is organized as follows. Section 2 presents
related work in software engineering, linking and com-
paring the metrology concepts and terminology adopted
in the International Vocabulary of Basic and General
Terms in Metrology [1], ISO 15939 [16], and ISO/IEC
25021 [20]. Section 3 presents the four steps proposed by
Abran [2] to design a measurement method. Section 4
analyzes the designs of two software measurement methods
from the literature. Section 5 concludes the paper with a
2. Related Work on Measurement Concepts
and Terminology
2.1. Metrology
The domain of knowledge referred to as metrology forms
the foundation for the development and use of measure-
ment instruments and measurement processes in the sciences
and in engineering.
While metrology has a long tradition of use in, for
example, physics and chemistry, it is rarely referred to in
the software measurement literature. A notable exception
in the software engineering literature is NIST (National
Institute of Standards and Technology), which investi-
gated “the underlying question of the nature of IT me-
trology” in 1996 [21], and identified “opportunities to
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Software Measurement Methods: An Analysis of Two Designs 799
advance IT metrology.” NIST proposed, for instance,
“logical relationships between metrology concepts,” con-
sisting of four steps to follow to obtain measured values:
defining quantities/attributes, identifying units and scales,
determining the primary references, and settling the secon-
dary references. In addition, in 1999, Gray [22] discussed
the applicability of metrology, and the necessity of ap-
plying it, from the software measurement point of view:
“We are still perhaps on the eve of giant steps in the new
century for information technology. We will still need
better measurements and more uniformity, precision, and
control to achieve these giant steps.” Since then, metrology
has been used for the design of the COSMIC measure-
ment method, and is also addressed in [2].
2.2. Measurement Definitions for the Practical
While in the software engineering literature, measure-
ment is often defined as a mapping between two struc-
tures, this does not give sufficient information about how
to measure in practice. It was pointed out in [2,23] that it
is necessary to move beyond the theoretical definition of
the mapping to an operational procedure, as described in
the vocabulary of the VIM [1] and modeled with a transi-
tion through three levels for a practical view (Figure 1).
A measurement principle forms the scientific basis of
measurement. For software entities (products), the measure-
ment principle involves the model(s) used as a basis to
describe the concept that is related to a concept to quan-
tify, and which can be quantified by a measurement
method. The idea is that modeling, as a central notion in
software products, should be considered at the same level
as scientific principles in other sciences and in engineer-
ing [2,23].
2.3. Base Quantity and Measurement Method
To adequately quantify a concept, a measurement method
Figure 1. Measurement foundations [1,2].
is required, which itself must include a coherent set of
definitions and measurement rules, as well as a base unit
specific to the measurement method as described in the
VIM [1]—Figure 2:
A base unit is “a measurement unit that is adopted by
convention for a base quantity” [1]. There is only one
base unit for each base quantity.
A measurement method is a generic operational de-
scription, i.e. a description of a logical sequence of opera-
tions for performing a measurement activity, for mov-
ing on from the concept to quantify to the value repre-
senting the measurement result [1, s. 2.5].
A measurement procedure is a set of operations, de-
scribed specifically and used in the performance of par-
ticular measurements according to a given method [1, s.
A measurement method should be implemented con-
cretely by some concrete operations achieved through
measuring instruments and/or practical operations: selec-
tion, counting, calculation, comparison, etc. This descrip-
tion of a measurement according to one or more measure-
ment principles and to a given measurement method is
called the measurement procedure, which is more spe-
cific, more detailed, and more closely related to the en-
vironment and to the measuring instruments (e.g. tools)
than the method, which is more generic.
Measurable concept: functional size for length
in the ISO 14143-1 standard [15].
Base quantity: 100 data movements in the COS-
MIC measurement method.
Base unit: a data movement from a single data
group in the COSMIC measurement method.
Concept to quantify: the Functional User Re-
quirements (FUR) in the ISO 14143-1 standard.
Symbol: CFP (COSMIC Function Points) in the
COSMIC measurement method.
Box A: Examples of some measurement terms in
software engineering.
Box A gives examples of a base quantity, a base unit, a
concept to quantify, and a measurable concept.
Note that the term metrics is avoided in the definitions
above: although it is widely used in software engineering,
Figure 2. A base quantity, as defined in the VIM [1].
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Software Measurement Methods: An Analysis of Two Designs
its use causes ambiguity, and possibly confusion, by sug-
gesting erroneous analogies; therefore, this term is not
used in this text.
2.4. Vocabulary Issues in ISO 15939
In 2002, the ISO documented and adopted a generic
model for the measurement process in software organiza-
tions in ISO 15939 [16] (revised in 2007). Specifically,
ISO 15939 “identifies the activities and tasks that are
necessary to successfully identify, define, select, apply,
and improve software measurement within an overall
project or organizational measurement structure” [16]. It
also provides “definitions for measurement terms commonly
used within the software industry,” using the VIM as its
base, although with some tailoring of the terminology to
facilitate it acceptance within the software engineering
In ISO 15939, a base measure is “a measure defined in
terms of an attribute and the method for quantifying it”
[16]. The right-hand side of Figure 3 presents definitions
of the terms adopted in this standard [16].
To obtain a base measure in practice, a measurement
method must be applied to an attribute of an entity (i.e.
an object which is itself a model of an object). In the
VIM, a measurement method is defined as “a generic
description of a logical organization of operations used in
a measurement” [1, ref. 2.5], while in ISO 15939, this
definition has been tailored as follows: “a logical se-
quence of operations, described generically, used in quan-
tifying an attribute with respect to a specified scale” [16].
Both definitions consider “a logical sequence/organization
of operations,” and from this perspective they are similar.
In ISO 15939, the attribute is a property of an entity. In
[2], the entity refers to “the concept to quantify,” which
should be related to a base unit [1]. The expression “base
unit” cannot refer directly to the expression “base measure”,
since a base unit is a part of a measurement method with
rules and conventions designed to obtain a “base quan-
tity.” In other words, a base quantity is a combination of
a number from the numerical world and a base unit es-
tablished by convention. For example, by international
convention in the SI, the base quantity of length is
Figure 3. A base measure, as defined in ISO 15939 [16].
composed of a number associated with the base unit
“meter”. To date, there has been little work done to de-
fine base units in software engineering, including base
units for the measurement of the quality of a software. In
software measurement, the COSMIC functional size mea-
surement method in ISO 19761 is unique, in the sense
that it has explicitly defined its base unit, referred to as
“a data movement of a single data group,” and its corre-
sponding measurement symbol, “CFP”. With this defini-
tion, a COSMIC measurement can be expressed as a base
quantity in the metrology sense with a number of base
units (for example, 15 CFP, 27 CFP, etc.).
In software engineering, the term time may refer to the
number of months representing the base quantity for ex-
pressing the concept of effort (as in productivity: soft-
ware delivered per work effort unit, measured in per-
son-months), or it may refer to the concept of duration
(often measured in calendar-months). The interpretation
of the measurement unit “month” will differ, depending
on the concept to be represented and measured (e.g. per-
son-months for the concept of human effort, and calen-
dar-months for the concept of project duration).
For the measurement of software quality, the measure-
ment units of quality concepts, like faults, errors, defects,
failures, etc., also need to be explicitly, and uniquely, de-
fined. There are other similarities and differences in the
terms used in the ISO 15939 and VIM vocabularies:
1) The concepts of fault, error, and defect:
a) Can be associated with the term “attribute”, because
they are properties or characteristics of an entity (i.e.
b) But are difficult to quantify, even when there is a
consensus on the corresponding base units (1 defect and
1 error, for example): it is not certain whether or not their
identification is unique (reproducibility and repeatability
2) The definitions of these “attributes” are generally
high-level definitions without corresponding explicit mea-
surement methods.
3) ISO 24765 (System and Software Engineering Vo-
cabulary) [19] provides the following definitions:
a) An error is defined as “a human action that pro-
duces an incorrect result, such as software containing a
b) A failure is defined as “an event in which a system
or system component does not perform a required func-
tion within specified limits”;
c) A fault is defined as “a manifestation of an error in
d) A defect is defined as “a problem which, if not cor-
rected, could cause an application either to fail or to pro-
duce incorrect results [19].
Each of these definitions refers to another definition
(e.g., an error contains a fault, and a fault is a manifesta-
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Software Measurement Methods: An Analysis of Two Designs 801
tion of an error), which adds to the difficulty of quanti-
fying concepts like these, and, based on these definitions,
of obtaining accurate measurement results.
The terms “concept to quantify” and “base quantity”
are used in [1] instead of “attribute” and “base measure”
respectively in [16,20]:
Furthermore, if “defect” had been selected as a base
unit in [16,20], this would mean that the concept of the
defect was used both a base unit and a base quantity. It
would be like using “length” and “meter” as a single
concept, while they are clearly distinct concepts, but, of
course, related in a well-organized relationship: “length”
is the concept to be quantified, and “meter” is the base
unit used for quantifying “length”.
In conclusion, the definitions of “attribute” and “base
measure” in [16,20] do not refer to an explicit definition
of a base quantity, or to an explicit corresponding measure-
ment unit. The proposal in [2] to use an explicit process
to design a measurement method with its base measure
(and corresponding base unit) can help improve measure-
ment in software engineering, but the software engineer
cannot expect the same precision in the short term as that
provided by the International System of Units.
2.5. Vocabulary in ISO 25021
ISO 25021 [20] is a part of the ISO 25000 series, which
is being published to update the ISO 9126 series [17].
ISO 25021 [20] has adopted a different vocabulary. For
example, the new expression “Quality Measure Element
(QME)” was substituted for “base measure”, and “pro-
perty to quantify”, for the term “attribute”. On the right-
hand side of Figure 4, a definition of each term has been
added from the ISO 25021 vocabulary to help the reader
understand the new terminology introduced.
According to ISO 25021, the user of the measurement
method shall identify and collect data related to the pro-
perty to quantify (Figure 4). Depending on the context of
usage and objective(s) of the Quality Measure Element
Figure 4. A Quality Measure Element (QME), as defined in
ISO 25021 [20].
(QME), a number of properties and sub properties can be
identified. These properties constitute the input to the
design of the measurement method, and are extracted and
defined from the artifacts of the software (e.g., docu-
mentation, code). This process2 is similar to the ISO
15939 process, but with a different terminology: “prop-
erty to quantify” instead of “attribute”, and “quality
measure element” instead of “base measure”.
2.6. Summary Mapping of the Three ISO
Reference Documents
A summary mapping of the measurement-related con-
cepts defined in these three ISO reference documents is
presented in Table 1.
The metrology vocabulary (VIM) is adopted here, because
it enjoys a wider consensus across the sciences and en-
gineering than the adaptations in the other two docu-
ments, which are limited to the software engineering
3. The Measurement Method
In this section, the four steps recommended for designing
a measurement method for a base quantity are described
in more detail [2]. In Section 4, we analyze, using these
steps, the design of two base quantities related to the
quality of the software.
To obtain a base quantity [1], it is not only necessary
to apply a measurement method to the measurable con-
cept, but also to use the base unit in the measurement
method, and to identify and define that base unit if this
has not already been done. Now, when measuring in
practice, a measurement procedure should be documented
as a distinct activity. This is because the measurement
procedure used to obtain the measurement result (i.e. a
base quantity) in a specific environment is required in
order to instantiate the measurement method (e.g., a pro-
cedure to determine the functional size of a project using
the COSMIC measurement method with use cases).
The four steps recommended by Abran in [2] to design
a measurement method are:
1) Determine the measurement objectives;
2) Characterize the concept (and the subconcepts) to
be quantified;
Table 1. Mapping between measurement-related terms.
VIM ISO 15939 ISO 25021
Concept to quantifyAttribute Property to quantify
Measurement methodMeasurement method Measurement method
Base unit
Base quantity Base measure Quality measure
2The word “process” is used because the references suggest a number
of steps.
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Software Measurement Methods: An Analysis of Two Designs
3) Design the metamodel (of the relationships among
the subconcepts);
4) Define the numerical assignment rules.
These steps can also help to verify the design of the
measurement method for a specific base quantity. As
well, they can be applied to specify or improve the de-
sign of measurement methods for many of the base quan-
tities3 embedded in the metrics proposed in ISO 9126.
3.1. Determine the Measurement Objectives
The first step is to identify the objectives for measuring
the base quantity. In ISO 9126, these objectives are re-
lated to the quality characteristics and sub characteristics
to be measured. The measurement context determines the
type of user of the base quantity, the life cycle phase in
which it will be used, and the number of constraints to
using it when the information is available.
3.2. Characterize the Concepts (and
Sub-Concepts) to Be Quantified
Software is often perceived as an intangible product, but
one that can be made visible through multiple representa-
tions: a set of screens and reports for a user, a set of lines
of code (or executable statements) for a programmer, and
a set of software model representations for a software
designer are some examples [24].
Characterization can be achieved by first stating ex-
plicitly how the concept (e.g., defects in the software do-
cumentation) to be quantified (e.g., defect in the software
documentation) is decomposed into sub-concepts (e.g.,
how defects in the software documentation are decom-
posed into sub-concepts).
Knowledge about the objective should determine what
information should be included in the quantification of
the concepts to be measured, or excluded from it, in
terms of sub-concepts. Moreover, it is important to care-
fully define what is included, as failure to do so can re-
sult in sub-concepts that are defined differently being
included in the design of measurement methods attempt-
ing to measure the same concept. For example, Base Func-
tional Components (BFC) are different in the IFPUG
standard [25] and the COSMIC Measurement Manual
[24]: IFPUG considers an elementary process (such as an
IFPUG Input or Output) as a BFC, while COSMIC con-
siders a data movement as a BFC. This makes it chal-
lenging to compare the results of these measurement
3.3. Design the Metamodel
Defining concepts and sub concepts is only one part of
the method for characterizing them. It is also necessary
to apply principles and set rules. Principles link the com-
pliance of a specific concept (or subconcept) to its defini-
tion. For example, an entry data movement in the COS-
MIC measurement method “shall not exit data across the
boundary, or read or write data.” Rules help to confirm
the status of a concept (or subconcept) in a particular
situation. For example, the trigger (a subconcept) of an
entry data movement could be the internal clock of a
computer, even though it is generated periodically by
hardware. Having defined the sub concepts related to the
concept to be quantified, the next step is to construct the
metamodel of the measurement method.
The metamodel is constructed based on the subcon-
cepts of the concept to be quantified. The relationships
(or roles) between that concept and the sub-concepts that
represent the software, or part of it, constitute the meta-
model. The metamodel describes how to recognize the
concept(s) and/or subconcepts in the measurement method.
For example, definitions, principles, and rules are de-
scribed in detail in the COSMIC Measurement Manual
[24] for determining the functional size of requirements
in the COSMIC measurement method.
A generic metamodel should not be specific to any
particular software, and must be independent of the spe-
cific context of the measurement, i.e. how the software is
implemented (unless it is what we want to measure). For
example, in the measurement metamodel of ISO 19761
(COSMIC), the functional user enters and receives data
that are read and written by software. This metamodel,
which is depicted in Figure 5 [24], shows the relation-
ships between the sub concepts (i.e. users, type of data
movement—entry, exit, read, or write) of the software
that use different physical components (I/O hardware,
computation hardware, and storage hardware. It should
also identify the measurand (input).
Each type of data movement in the COSMIC meas-
urement method rules is considered as an input (i.e. the
measurand) to be taken into account in the measurement
3As mentioned in Section 2, some base quantities in ISO 9126 are dif-
ficult to relate to a measureable concept, and have no base unit. Figure 5. COSMIC metamodel [14,24].
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Software Measurement Methods: An Analysis of Two Designs 803
3.4. Define the Numerical Assignment Rules
Assigning numerical rules is part of the process of de-
signing a measurement method. A numerical assignment
rule can be described from a practitioner’s point of view
(generally text) or from a theoretical point of view (gen-
erally a mathematical expression).
A quantity should be associated with a scale type [2].
Only certain operations can be performed on certain scales
of measurement, and the mathematical algorithm pro-
posed by a measurement method must conform to those
operations. For example, differences between two ordinal
values cannot be quantified; therefore, adding ordinal
numbers is not allowed. When the scale types are not
taken into account accurately, the quantities obtained could
be wrongly interpreted.
The purpose of the measurement determines the usage
of the base quantity and which base unit should be used.
This affects the definition of the numerical assignment
rules. For example, to obtain the number of COSMIC
function points, it is necessary to identify a base unit. In
COSMIC, the base unit is defined as a data movement
that is related to different types of data movement (Entry,
Read, Write, and Exit) within a functional process.
4. Analysis of the Designs of Two Software
Measurement Methods from the
There are hundreds of definitions of software metrics in
the software engineering literature, but only a few attempts
have been made to provide comprehensive definition of a
measurable concept for a measurement method. We have
chosen two designs of software measurement methods,
because their definitions are documented and are both
related to software quality:
1) The measurement method for code, from Munson
and Nikora [26];
2) The measurement method for the size of “use cases
from the documentation”4 in [27].
Using the measurement concepts and criteria in [2,26],
it is possible to determine whether or not the measure-
ment method proposed for the concept to be quantified is
complete. This section discusses how each example fulfills
the requirements for each step in the design of a measure-
ment method.
4.1. Fault in [26]
Step 1: Determine the measurement objectives
The information related to the first step is found in the
Introduction and in Section 3 of [26]:
- In their introduction, Munson & Nikora wrote: “We
have developed a method for unambiguously identi-
fying and counting faults.” More specific objectives
are listed in Section 3.1—“The subject of this paper is
the identificatio n and en umera tion o f fau lts tha t oc cur
in source code5.”
Comments on Step 1:
- Munson & Nikora point out that it is necessary to
develop a measurement method to identify faults.
While a measurement method is not required for
counting (determining the number of chairs in a
classroom, for example), it is not possible to calculate
the surface area of a desk without using a measure-
ment method and a measurement procedure. By
analogy, it would be challenging to accurately quan-
tify the faults in software without a measurement
method. However, the sentence that links the phrases
“develop a method” and “counting faults” is ambigu-
In the first step of the measurement method, “the mea-
surement context determines the type of users of the base
quantity, the life cycle phase in which it will be used, and
the number of constraints to using it when the informa-
tion is available.” The user is not mentioned directly in
[26], but we can assume it is the developer. The life cycle
phase is most probably the “coding phase,” based on the
method’s purpose. Finally, in Section 3 in [26], it is pos-
sible to identify the constraints to finding faults: 1)—“We
will base our recognition and enumeration of software
faults on the grammar of the language of the software
system”; 2)—“The granularity of the measurement for
faults will be expressed in terms of tokens that have
changed; 3)—“Rulesbased on the types of changes
made to source code in response to failures reported in
the system.”
Step 2: Characterize the concepts to be measured
A number of concepts related to faults are proposed in
[24], through definitions and redefinitions of the term in
Sections 1 through 3:
- A fault is defined as a structural imperfection in a
software system that may lead to the systems eventu-
ally failing (Section 1).
- A fault is a manifestation of an error in software
(Section 2).
- In Section 3: “If any of the tokens changes that com-
prise the statement, then each of the change tokens
will represent a contribu tion to a fault count.”6
- In Section 3: “The granularity of measurement for
faults will be in terms of tokens that have changed.”
- A fault is “an invalid token or bag of tokens in the
source code that will cause a failure when the com-
4The initial document was written as a term assignment for Dr. De-
sharnais’ measurement course given at the Middle East Technical Uni-
versity, Fall of 2009 Semester, and summarized in [2]. See reference
5Source code is the equivalent of “measurand” in [1].
6This sentence is ambiguous and it should probably read: If any of the
tokens that comprise the statement changes, then each of the changed
tokens will represent a contribution to a fault count.
Copyright © 2012 SciRes. JSEA
Software Measurement Methods: An Analysis of Two Designs
piled code that implements the source code token is
executed” (end of Section 3).
Comments on Step 2:
- The concept of error is introduced in Section 2, but is
never used again in the text. We can assume that the
authors prefer to define a fault as a structural imper-
- Defining the concept of fault is a requirement for de-
veloping a measurement method, but a “precise defi-
nition of what faults are made of” does not constitute
such a definition. In Section 3, the concepts of state-
ment (executable) and token (change) are introduced
as part of “a contribution to a fault count.” More pre-
cisely, this contribution is explained in the definition
of a fault at the end of Section 3 in relation to the
concept of failure, when a “code token is executed.”
This redefinition also introduces the term bags of to-
- Not all changes are necessarily errors. If this were so,
then the aim of counting the errors is not achieved,
mainly because the number of errors may not equal
the number of changes. The mathematical equation
cannot give the correct result, because it lacks some-
thing. This is acknowledged by the authors in Section
7 (Discussion and Future Work): “It is clear that
noise in the fault measurements may have a signifi-
cant effect on our results…”; “We must be careful to
se lec t representative failures…”; “Our definition could
again lead to undercounting the number of faults re-
Step 3: Design the metamodel
Relationships between concepts and sub concepts are
to be provided. This will lead to a better understanding of
the metamodel, but also determine the way to quantify
the attribute.
From Section 3 of [26], software faults are to be recog-
nized as follows:
- They must be found in statements, both executable
and non executable;
- They are defined as changes in lines of code as a result
of a failure event in a module program;
- Every line of text in every version of the program can
be seen as a bag of tokens;
- There is a possibility that there will be multiple tokens
of the same kind on each line of the text;
- A change to be made in a line of code by a developer
is a response to the detection of a fault, either through
normal inspection or a code review process (non execu-
table), or as a result of a failure event in a program
module (executable).
It is possible to find a schema of the metamodel in
Section 6 (Current Application) of [26]. Figure 6 sche-
matically represents the fault definition as applied to a
JPL software development effort [26]. This is the way
Figure 6. Metamodel of faults derived from [26]: relation-
ships among the sub concepts of faults.
the authors describe how the problems are reported:
“For each failure reported through the system, a ‘change
package’ is automatically opened in the repository. De-
velopers then check the repairs in the change package,
and commit the completed change package to the reposi-
tory when the repairs have been completed. In this way,
it is possible to identify the changes that were made in
response to each failure that was reported” (Section 6,
second paragraph).
This leads to a specific definition of a software fault
and to the way to recognize a software fault in [26]: a
software fault is “an invalid token or bag of tokens in the
source code that will cause a failure when the compiled
code that implements the source code token is executed.”
Executable statements (lines of code), tokens, bags of
tokens, bag cardinality, and bag differences are sub con-
cepts of the fault, or different concepts to be used in the
measurement method.
Comments on Step 3:
- There is no schema provided in [26], only a text and a
figure from a CVS application. Here, Figure 6 at-
tempts to model these explanations.
- It is still possible that the schema in Figure 6 does
not represent the real application correctly.
- In [26], the metamodel is implicit, and not explicitly
described. A specific measurement procedure was
applied in the example provided, but there is no way
to know if the measurement result reflects the implicit
Step 4: Define the numerical assignment rules
The granularity of measurement for faults is proposed
in terms of tokens that have changed. Because the term
token can be expressed in different programming languages,
Copyright © 2012 SciRes. JSEA
Software Measurement Methods: An Analysis of Two Designs 805
Table 2. The token change concept.
1) a = b + c; (5 tokens)
2) a = b – c; (5 tokens)
Need to change + by –
1 token change
its definition remains a part of the measurement method.
As observed in Table 2, the concept of change in [26] is
related to the number of tokens changed in a statement.
A, =, b, +, c are tokens of statement 1.
The only change in statement 2 is the token +, which is
replaced by the token.
The measurement method described in [26] has the
following assignment rules to obtain the number of soft-
ware faults:
- A unit of measurement is assigned to every token
change in the code;
- To obtain the number of faults, the measurer adds up
the token changes;
- Actually, one changed token constitutes one unit;
- There is a measurement rule for adding each change
automatically. The example in [26] is related to the C
programming language;
- As each token change is expressed as one unit, the
result of adding token changes can be considered as a
ratio scale type.
Comments on Step 4:
There is room for improvement to the measurement
method proposed in [26], as follows:
- Identify the base unit: the token;
- Impose a rule to obtain the number of faults (token
changes), the clear choice being: add up the token
- Complete the set of rules for finding a fault, which is
currently incomplete. For example: if a = 1 + c + b is
changed to a = 1 + b + c, how many faults should be
counted, considering that the user sees no change in
the results (i.e. there is no failure).
The proposal in [26] constitutes one of the rare efforts
to propose a measurement method related to the quality
of software. However, based on the previous comments,
the metamodel and the measurement rules can be improved.
4.2. Use Case (Ozcan Top)
This sizing of use cases as an example of the design of a
base measure can be found in [27] [2, ch. 4, pp. 87-91].
Step 1: Determine the measurement objectives
In the Measurement Objective section, the author states:
The aim of this measurement method is to measure the
size of the case.” Again, “the results of this measurement
will also be helpful in assessing the internal quality, ex-
ternal quality, and quality-in-u se of a software product.”
Finally, the measurement method “can be used by soft-
ware developers, software managers, and customers.” [27]
The results of the measurement can even be applied in
the early phases of a software life cycle, i.e. when use
case requirements are available.
Comment on Step 1:
- The measurement objectives are clearly formulated.
Step 2: Characterize the concepts to be measured
The measurable concept is size, but size is related to
the use cases. So, because use cases are related to require-
ments, size is an indirect quantification of the requirements.
A use case is “the description of the interaction be-
tween an Actor (the initiator of the interaction) and the
system itself. It is represented as a sequence of simple
steps. Each use case is a complete series of events, de-
scribed from the point of view of the Actor. Actor, Main
Scenario, Alternative Path s (Extensions), and Exceptions
are the concepts of the measurement method” [27].
- The author has defined the various “events” in Table 3;
- The subconcepts are input, process, and output;
- The input is “any item, whether internal or external to
the project, that is required by a process before that
process procee ds .”
- The output is the “data transmitted to an external
destination” or “a product, result, or service generated
by a process.”
- The process is “a set of interrelated or interacting
activities which tran sforms inputs into outputs.”
The author presents the various event types from a use
case template:
Table 3. Use case template [27].
Use case ID
Use case name
Creation date
Modification date
Flow diagram
Frequency of use
Main scenario
Alternative paths
Notes and issues
Copyright © 2012 SciRes. JSEA
Software Measurement Methods: An Analysis of Two Designs
Copyright © 2012 SciRes. JSEA
The mathematical formula is the following: Comment on Step 2:
- A number of event types can be found in the defini-
tion of the use case (Table 2), and from there, it is
possible to define an action as the base unit.
Step 3: Design the metamodel
Number of Cases = Σ number (Input Actions) + Σ
number (System Actions) + Σ number (Output Actions)
The measurement model of the size of the require-
ments in a use case is presented in Figure 8.
- The metamodel puts together the various functional
requirements (concepts to quantify), the use cases (ob-
jects targeted by the measurement procedure), the
events, and the base units from the different types of
actions. Figure 7 presents those relationships.
Comment on Step 4:
The measurement method is theoretical because no tests
(i.e. measurement exercises) have been performed using
it to evaluate its performance as a measurement method.
5. Discussion
- The use cases (objects) define the requirements (con-
cepts to quantify), which consist of events that can be
translated into different types of action (base units).
Comment on Step 3:
In the software engineering literature, few references
focus on the definition and design of software measure-
ment methods. Among those that do are Munson, et al.
[26] and the ISO standards on functional size measure-
ment [14,15,27,28]. To avoid inconsistent vocabulary
and potentially incorrect interpretation of data, software
measurement methods must be better designed, including
definitions, measurement principles, measurement rules,
and base units.
- Figure 7 presents an overview of how the measure-
ment result is derived from the application of the
measurement method proposed in [27]. Its title, “Use
case method, main concept, and subconcept meta-
model,” is not strictly accurate, however, because
Figure 7 represents events, concepts, and subcon-
cepts as concurrent.
Step 4: Define the numerical assignment rules. The
action is “the element of a step that a user performs during a
Well-designed measurement methods are necessary for
each of the 80 base measures embedded within the 250
or more derived measures referenced in ISO 9126 [18],
in particular those related to: defect, fault, error, failure,
error message, warning message, illegal operation, data
correction, and fault pattern. Many others could be de-
signed for use in conjunction with the base measures
related to quality aspects like memory size, effort, dura-
tion, and size of the product.
As such, the action could be considered as the base unit.
The number of cases is calculated by adding up the
various types of actions (Input Action, System Action,
and Output Action). According to the measurement func-
tion, each of these action types is assigned a numerical
size of 1 Action Point (AP).
Figure 7. Use case method, main concept, and subconcept metamodel from [27].
Software Measurement Methods: An Analysis of Two Designs 807
Figure 8. Measurement model of the measurable concept (number of actions in use cases) from [27].
Further research is necessary to define and design the
base measures used in quality models, productivity models,
and estimation models, among others.
Each of the three ISO documents that we reference
here uses a different terminology to structure and/or to
analyze measurement methods, and three needs have been
identified in the analysis presented in this paper:
The need to establish a unified vocabulary for the
main measurement concepts, and to relate it to the
major literature sources in a coherent manner;
The need to detail the very first phase of the meas-
urement life cycle, i.e. the design of a measurement
The need to derive verification criteria for software
measurement methods.
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Copyright © 2012 SciRes. JSEA
Software Measurement Methods: An Analysis of Two Designs 809
Appendix 1 [26]
This table provides an example of a use case in UML.
Copyright © 2012 SciRes. JSEA