Analysis of Software Measures Using Metrology

Concepts – ISO 19761 Case Study

Alain Abran and Asma Sellami

École de technologie supérieure – ETS

Université du Québec, Montréal, Québec, Canada

Abstract. To help identify the strengths of proposed software measurement

methods, this paper proposes an analytical approach based on metrology con-

cepts documented in the ISO International Vocabulary of Basic and General

Terms in Metrology. This approach is illustrated with a case study using one

specific functional size measurement method recognized as an ISO standard:

COSMIC-FFP (ISO 19761). The case study documents the metrology concepts

addressed in this ISO standard, either in the design of this measurement method

or in some of its practical uses. It illustrates, for instance, that the design of

COSMIC-FFP encompasses a large number of related metrology concepts. It is

suggested that such a review using metrology criteria be used to analyze other

software functional size measurement methods, as well as other software meas-

ures suggested to industry.

1 Introduction

Hundreds of software measures have been defined in the software engineering

domain and proposed to industry. However, only the following have successfully

undergone the rigor of international standardization: the quality measures in the ISO

9126 series [8], and three functional size measurement methods, among them ISO

19761 – COSMIC-FFP [10]. Software functional size measures are used in particular

to compare the productivity of software projects (internally or across organizations),

for project effort estimation and for the control of functional changes over a project

life cycle. The use of such standardized measures is important to ensure comparabil-

ity of measurement results between projects and between organizations; indeed, it

would not be relevant to compare numbers based on distinct (and not standardized)

measurement methods. Without the use of standards, ideally those officially recog-

nized internationally, software agreements between customers and suppliers are prone

to a variety of interpretations and, often, to conflicts.

A large number of software measures are defined based on the intuition of their au-

thors. W

hen subjected to the scrutiny of researchers, they are often investigated only

from the perspective referred to as “measurement theory” (i.e. their mathematical

properties) [5, 6, 11]. However, in other science and engineering disciplines, it is the

domain of knowledge referred to as “metrology” that is the foundation for the devel-

Abran A. and Sellami A. (2004).

Analysis of Software Measures Using Metrology Concepts – ISO 19761 Case Study.

In Proceedings of the 1st International Workshop on Software Audits and Metrics, pages 69-84

DOI: 10.5220/0002685500690084

 SciTePress

opment and use of measurement standards, measurement instruments, and measure-

ment processes [3].

In this paper, we propose to use our initial modeling [2] of the sets of measurement

concepts documented in the ISO International Vocabulary of Basic and General

Terms in Metrology – VIM [7] to investigate whether or not the full set of metrology-

related concepts has been taken into account in the design and application of software

measures. To illustrate this approach, one specific type of software measure, that is,

COSMIC-FFP (ISO 19761), a functional size measurement (FSM) method, has been

selected as a case study. This choice was based on the following criteria: 1) when

compared to other types of software measures, FSM methods are supported by much

more detailed operational descriptions than those for most other software measures;

2) only software measures of this type have undergone the rigor and scrutiny of inter-

national standardization and have reached the status of official ISO standard (it

should be noted that the ISO 9126 series, with its set of definitions of quality meas-

ures, is an ISO technical report rather than an international standard per se).

This paper will therefore use ISO 19761 [10] for illustrative purposes to explore

whether or not such a software measure encompasses most – if not all – of the classic

metrology concepts.

The paper is organized as follows: Section 2 presents an overview of the metrol-

ogy concepts documented in the VIM and of a specific FSM method, ISO 19761

standard (COSMIC-FFP). In section 3, metrology-related concepts are identified in

the design of COSMIC-FFP; in section 4, measurement process-related concepts are

described; and in section 5, measurement instrument-related and measurement re-

sults-related concepts using an RUP/COSMIC-FFP-related software prototype tool

are presented. Section 6 contains a summary of this analysis of COSMIC-FFP with

respect to metrology, along with some concluding observations.

2 Overview of VIM and COSMIC-FFP

2.1 Metrology - VIM

Metrology is the science of measurement [7] and includes the set of methods de-

signed to perform the measurements and to provide a sufficient level of confidence in

the measurement results. To carry out a measurement, it is necessary to compare an

unknown quantity with a quantity of the same kind which has become a reference

through quantification by a measuring instrument. Metrology encompasses all aspects

of measurement (theoretical and practical) according to a measurement method de-

sign and in all domains of science and technology.

Six categories of metrology concepts are described in ISO VIM [7]:

1. Quantities and units

2. Measurements

3. Measurement results

4. Measuring instruments

5. Characteristics of the measuring instruments

6. Measurement standards – Etalon

Our initial modeling of the interrelated terms of this vocabulary, organized by cate-

gory as above, is presented in Appendix A, either in the form of process models

where appropriate, or in structured tables when the interrelated terms are, for in-

stance, enumerative. In particular, the expression “topology of concepts” has been

used to highlight the existence of links between related concepts. In this paper, we

use the models and tables in Appendix A extensively to analyze not only the design

of the COSMIC-FFP measurement method, but also the application of this FSM

method.

Two of the six metrology categories of concepts are related to some aspects of the

design of measurement methods, that is: “quantities and units” and “measurement

standards - etalon”. The other four categories are related not to the design of a meas-

urement method itself, but rather to the application of a measurement design with a

measuring instrument and to the quality characteristics of the measurement results

provided by this measuring instrument (including the inherent related degree of un-

certainty of the measurement results).

2.2 Overview of COSMIC-FFP

Software size can be assessed either by measures of length (for example, lines of

source code in a module, pages in a requirements specification document) or func-

tionality (for example, function points). Functional size measures can be derived

directly from the specifications and can be obtained fairly early in the development

life cycle, which makes them useful both for planning purposes and during the whole

project life cycle.

The first generation of FSMs was developed in the late 1970s, followed by a large

number of variants. It is only in the early 2000s that a second generation of such

measures has emerged and been rapidly adopted as an international standard [10]:

ISO/IEC 19761: 2003 COSMIC-FFP: A functional size measurement method. This

FSM method is based on the application of a set of models, rules, and procedures to a

given piece of software, as it is defined from the perspective of its Functional User

Requirements – FURs. By design, the measurement results provided by this method

are independent of the technology. This ISO FSM standard is suitable for measuring

various types of software (business application software, real-time software or Web-

based and Internet applications, and so on), independent of technologies, develop-

ment, and implementation decision approaches. By design, and in conformity with

ISO 14143-1 [9], the standard is independent of the implementation decisions em-

bedded in the operational artifacts of the software to be measured and excludes both

the software quality and technical characteristics.

COSMIC-FFP takes into account that software FURs can be decomposed into a set

of functional processes, and that each of these functional processes constitutes a

unique set of data movements and/or data manipulations (Fig. 1). The COSMIC-FFP

software model distinguishes four types of data movement: entry, exit, read, and

write, as identified in the context model (Fig. 2). By convention, all data movements

move data contained in exactly one data group. Entries move data from the user

across the boundary to the inside of the functional process; exits move data from

inside the functional process across the boundary to the user; reads and writes move

data from and to persistent storage.

In COSMIC-FFP, each data movement is assigned a single unit of measure of 1,

which is, by convention, equal to 1 Cfsu (Cosmic functional size unit). The total size

of the software being measured corresponds, therefore, to the addition of all data

movements recognized by the COSMIC-FFP FSM method. See [1, 10] for the de-

tailed measurement rules.

Fig. 1.

A generic software model for

measuring functional size [1]

Manipulation

Boundary

Entry

Exit

Write

Read

Functional

process

Users

Storage

Fig. 2. COSMIC-FFP Movement types [1]

: Data movement type

sub-processes

Functional User

Requirements

Data Movement

type

Data Manipulation

type

Sub-process types

Softwa re

Functional

Process type

3 Analysis of COSMIC-FFP design

3.1 Quantities and units

The first analysis focuses on the design of COSMIC-FFP using the set of metrol-

ogy concepts on “quantities and units”, as described in Table A.1 of Appendix A. The

results of this analysis are presented in Table 1. As can be observed from Table 1, the

design of COSMIC-FFP allows quantification of a (measurable) quantity (that is, a

movement of a single data group in a functional process) in well-defined units (that

is, Cfsu). However, the COSMIC-FFP standard does not yet include any derived

measure, and its system of quantities comprises a single base quantity, that is, the

Cfsu itself.

The symbol for the base COSMIC-FFP quantity is the visual representation of

"Cfsu", and this symbol is used to represent the unit of measurement, or 1 Cfsu. In the

current state of the art for FSM, there is again only one unit of measurement, that is,

there are no derived or off-system units.

It should be noted next from Table 1 that there are not yet either multiples or sub-

multiples of a unit of measurement (like kilograms or centigrams). This lack of multi-

ples and submultiples applies to the other ISO-recognized FSMs as well. Similarly, in

COSMIC-FFP, there is only one level of granularity and formally recognized conven-

tional reference scale, which is the level of a single data group movement, no matter

how many attributes there are within this data group. The COSMIC Guide [1] recog-

nizes, however, that some measurers might want to define their own – nonstandard-

ized – finer levels of granularity (for example, at the level of data group attributes);

however, there is not yet a consensus on this topic, and therefore there is not yet a

basis on which to develop an international consensus for such a measurement conven-

tion.

In the last section of Table 1, the analysis of the set of concepts related to “value”

(of a quantity) is more complex because, in our opinion, it includes concepts related

both to the measurement method design and to its application in specific instances.

Table 1. Quantities and Units metrology concepts in COSMIC-FFP

Metrology [7] ISO 19761 [10] and COSMIC

Implementation Guide [1]

Clause in ISO 19761

[10]

System of quantities

(Currently, only one base quantity

is included)

Base quantity Cfsu

Derived quantity (none yet defined)

2.5 COSMIC-FFP

measurement phase

Dimension of a quantity

(not explicit)

Quantity of dimension one /

Dimensionless quantity

(undetermined)

2.7 Functional size

measurement context

Unit (of measurement)

= 1 Cfsu

Symbol of a unit = Cfsu

System of units Not applicable

Coherent (derived) unit Not applicable

Coherent system of units Not applicable

International system of units,

Not applicable

Base unit = 1 Cfsu

Derived unit None

Off-system unit None

Multiple of a unit None yet defined

Submultiple of a unit None yet defined

2.5 COSMIC-FFP

measurement phase

Value (of a quantity)

Value of functional size

True value Not yet explored

Conventional true value = In practice, obtained by expert

judgment

Numerical value = Result of a measurement: func-

tional size

Conventional reference scale/

Reference-value scale

= Scale = a data group movement

(independently of data movement

type, and number of data attributes

moved). Each data group movement

is assigned a value of 1 Cfsu

2.2 COSMIC-FFP

measurement process

model

Finally, a “conventional reference scale/reference-value scale” represents particu-

lar quantities of a given kind, an ordered set of values, continuous or discrete, and is

defined by convention as a reference for arranging quantities of that kind in order of

magnitude. In COSMIC-FFP, this concept corresponds to the scale of a movement of

a data group (entry, exit, read, and write, abbreviated by convention as “E” for entry,

“X” for exit, “R” for read, and “W” for write). Each movement of a data group has a

size of 1 Cfsu in COSMIC-FFP. There is, of course, a standard definition of what is

recognized as a “data group” by COSMIC-FFP. In addition, it represents a discrete

set of values composed of E = X = R = W = 1.

In COSMIC-FFP, the “numerical value” of the software to be measured corre-

sponds to the addition (in the same software layer) of the individual values assigned

to each identified movement of a data group. This addition provides the “numerical

value” of the software to be measured. In short, “numerical value” and “conventional

reference scale” are explicitly defined in the COSMIC-FFP standard [10].

3.2 Measurement standards – Etalon

In measurement for the sciences and for engineering, it is taken for granted that

there should exist “measurement standards - etalons” for calibrating and verifying the

measuring instruments and to ensure the consistency of measurement results across

individuals, organizations, and nations. However, this metrology concept has not yet

been discussed in the software measurement literature, nor has it been the focus of

attention of practitioners. In software measurement, what could be close to this con-

cept, and its related sub-concepts in Table A.4, are the case studies documented for a

few of these software FSM methods.

4. Analysis of Measurement with COSMIC-FFP

In the VIM, the term “measurement” refers to the category of terms for the “set of

operations” required to obtain a measurement result (see also Fig. A.1), and this is

instantiated through the generic measurement process described in Fig. A.2.

This figure illustrates, with the use of a graphical representation of a process, dif-

ferent concepts related to the concept of “measurement”. It should be noted that, in

metrology, the “quantity to be measured” by means of a set of operations (and a

measuring instrument) is also called a “measurand”, that is, the input quantity that is

applied to a measuring instrument (Fig. A.2).

As described in Fig. A.2, a measurement procedure requires, as input, a meas-

urand, which corresponds in COSMIC-FFP to the FURs, and produces a measure-

ment result which represents a numerical value of functional size. An instantiation of

a measurement procedure for a specific measurement includes an operator to carry

out the measurement process (here, the measurer), the measurement method itself

(here, the standard method), and the influence quantities (here, conditions that could

influence/ bias measurement results). The operator corresponds to the user of the

method (the measurer). The COSMIC-FFP measurement method is explicit, and the

influence quantities include, for example, user skills, capability of the given docu-

mentation to perform measurement, allocated time, etc.

In COSMIC-FFP, the quantity to be measured (the “measurand”), as determined

by the software users through the functional requirements (FURs), will be trans-

formed through the prescribed set of logical operations to provide a numerical value

(a number representing software functional size). This number is associated with a

size unit (Cfsu) to represent the measurement result (numeric value).

In the ISO standard for COSMIC-FFP [10], the standardized definitions of the

concepts relevant to this method are specified in Clause 3, while the logical sequence

of operations described as “measurement activities” are specified in Clause 6. In our

opinion, these definitions and measurement activities should meet the metrology

concepts for “principle of measurement” and “method of measurement” defined in

the VIM [7]. However, these two VIM concepts, which correspond to the foundations

of a measurement from a metrology perspective (Fig. A.1), are not described in finer

levels of detail in the VIM with a view to verifying whether or not there is a full cor-

respondence, in the COSMIC-FFP standard, of their underlying subconcepts.

It should also be noted that, in the software measurement literature, the concepts of

“measurement signal” and “transformed value” are not discussed explicitly. Even

though these two sets of terms are not discussed in the ISO standard [10], they are

explicitly presented and discussed in the COSMIC guide for the implementation of

the ISO 19761 standard [1]: they correspond to the set of concepts included in what is

categorized as the “mapping phase” between the documentation of the FURs and

their mapping to COSMIC-FFP. In an explicit way, this COSMIC guide [1] pre-

scribes that the transformed value be obtained by the following sequence of opera-

tions:

"The measurer should identify the boundaries of the software to be measured,

identify all functional processes, triggering events and data groups, map them in the

software context model using the COSMIC rules, identify the layers, identify the data

movements in each function process and sub-process, and determine the COSMIC

size measurement by adding the results." [1].

A summary of these correspondences of measurement metrology concepts in

COSMIC-FFP is presented in Table 2.

Table 2. Measurement metrology concepts in COSMIC-FFP

Metrology [7] COSMIC Implementation Guide of ISO 19761 [1]

Measurand An FUR in an artifact of the software to be measured

Measurement signal Mapping phase: measurement context and COSMIC-FFP software

models

Measurement procedure Measurement phase: rules and methods to be applied to the output

of the Mapping phase as represented in the COSMIC-FFP generic

software model

Measurement result Functional size of the generic software model of the FUR: nu-

merical value

Operator The measurer

Method of measurement See ISO 19761: COSMIC-FFP [10]

Influence quantity For example: measurer expertise, quality of FUR documentation,

time allocated for measuring, etc.

5 Analysis of COSMIC-FFP Measuring Instruments and

Measurement Results

To explore the metrology concepts relevant to the measuring instruments and

measurement results, we use as a case study the prototype of COSMIC-FFP devel-

oped in the RUP-Rational Rose environment, as described in [4].

5.1 Measurement standards – Etalon

In scientific and engineering (and also commercial) environments, measurement is

normally carried out using measuring instruments which are calibrated from reference

standards/etalons. As illustrated in Fig. A.3, for example, the “measuring chain”

represents the series of elements of a measuring instrument or system. In [4], the

equivalent of a measuring chain is described as including the path of the measurement

signal from the input as an FUR description of the Use Cases, the measurement proto-

type itself, and the output as the measurement results. More details of the mapping of

this case study are presented in Table 3.

The notion of the measurement scale is also within the set of concepts related to

the measuring instruments, and includes a dozen subconcepts, as illustrated in Fig.

A.7. However, the application of these metrology concepts essentially depends on the

presence of multiples and submultiples of a unit of measurement. Again, in the cur-

rent state of the art of software FSM, these subconcepts are not present and therefore

cannot be discussed here.

Table 3. Measuring Instrument metrology concepts and COSMIC-RUP prototype [4]

Metrology [7] COSMIC – RUP Prototype [4]

Measuring chain FUR + COSMIC-RUP prototype + functional size results in [4]

Measuring system: Complete set of elements of the software prototype + manual proce-

dures

Detector Prototype function which extracts the elements to be measured

Measuring transducer The mapping solution between COSMIC and UML-RUP concepts

in [4]

Measuring instrument In the COSMIC-RUP prototype, the set of functionalities to imple-

ment the COSMIC-FFP measurement rules

Material measure Measurement results, displayed on output screens and saved in

memory

Integrating instrument Not in the prototype (since it does not handle any 'other quantity')

Measurand Set of FURs

Another quantity Not in the prototype

Details of a measuring instrument:

Displaying/ Indicating

device (+index)

Display screens of measurement results

Recordin

inst

ument/ Prototype function, which allows recording in the database

Recording device

Note: not all details appear in this table

5.2 Measurement results

In all measurement instantiations, a measurement result is usually associated with a

measurement uncertainty, because, in practice, no perfect measurement process ex-

ists. Measurement uncertainty is defined in metrology as a parameter characterizing

the dispersion of the values that could reasonably be attributed to the measurand, that

is, the interval centered on the measured value and in which it is very probable that

the true value and the conventional true value will be found. In the current state of

software FSM knowledge, the true value is generally obtained by consensus among

measurement experts. The difference between the results obtained by a measurer (or

by a measuring instrument) and by an expert represents the error.

In [4], the measurement results of a case study are presented; however, it is a

small-scale case study only for the purpose of demonstrating the technical feasibility

of the automation concept of the COSMIC-FFP standard in the RUP/Rational Rose

environment. To obtain statistically significant results with information about the

concepts included in the detailed topology of measurement results, much larger case

studies will be required. Details of the mapping of this case study are presented in

Table 4.

Table 4. “Measurement Results” metrology concepts and COSMIC-RUP prototype [4]

Metrology [7] COSMIC – RUP Prototype [4]

Measurement result types

Indication Detailed results, summarized, according to the proposed

templates in [1]

Uncorrected result Measurement results, prior to human intervention to add

missing information

Corrected result Revised measurement results, after addition of missing in-

formation

Mode of verification of results

Accuracy of measurement In [4], this characteristic is only tested with a small-scale

case study. There are not enough cases to obtain significant

statistically quantitative knowledge of this characteristic

Repeatability A software tool normally provides the same results in repeat-

able conditions (needs to be verified by further experimenta-

tion)

Reproducibility Same as above

Uncertainty of measurement

and 8 other related concepts

Characteristic not yet explored

5.3 Characteristics of measuring instruments

We have modeled the “characteristics of measuring instruments” from both the

quantitative and qualitative viewpoints described in Table A.3.

5.3.1 Quantitative viewpoint

In the COSMIC-RUP prototype [4], several quantitative metrology concepts can be

observed: for example, in the description of its operational conditions (that is, the

FUR must be modeled according to an RUP process based on UML formalisms) and

of its boundary conditions (that is, the prototype currently deals with only one soft-

ware layer at a time). Further mappings are presented in Table 5.

Table 5. Quantitative viewpoint of “Characteristics of Measuring Instruments”

Metrology [7] COSMIC –RUP Prototype [4]

Rated operating conditions It is necessary to model FURs according to an RUP process

based on UML formalisms

Limiting conditions The prototype deals currently with only one software layer at a

time

Reference conditions

Example: a functional process must have more than 2 data

movements

Instrument constant The tool should preserve its metrological characteristics over

time (even, for example, when there is a change of version in

each of its software components)

Response characteristic

New levels of units of measurement have been defined in the

tool (Ufsu and Sfsu), but the response characteristics have not

yet been analyzed

Sensitivity A particular case has been identified; for example, to indicate

whether or not it is possible to categorize correctly the read or

write movements. It is recognized that this categorization prob-

lem does not have any impact on the final size itself since the

numerical value for each data group movement = 1 independ-

ently of its category (for example, sensitivity = none)

Discrimination (threshold) 1 Cfsu, the minimum size of a change to an FUR

Resolution (of display

device)

Not yet investigated

Dead band Not yet investigated

5.3.2 Qualitative viewpoint

In the COSMIC-RUP prototype [4], the results of the analysis between the qualita-

tive viewpoint of “characteristics of measuring instruments” from Table A.3 are pre-

sented in Table 6. It must be noted here that the mappings with the concepts of the

functionality test (use errors and control errors), and even the measuring range or

working range concepts (nominal range, span, and nominal value) have not been

explored, since the appropriate experimental conditions were not available. (See Ta-

ble A.3 for the list of related metrology concepts).

Table 6. Qualitative viewpoint of Characteristics of Measuring Instruments

Metrology [7] COSMIC-FFP: automated tool with RUP [4]

Stability Not yet investigated

Transparency COSMIC-FFP/ RUP prototype is a transparent instrument for the

measurement of a functional process

Drift Not yet investigated

Response time There is a time interval between the instant of the stimulus and the

instant of the response

Accuracy of a measuring

instrument

This was analyzed with only one case study, which was a small-

scale one. More case studies should be constructed and the results

analyzed to determine the accuracy of the results measured by the

prototype, and under which set of conditions

Accuracy class (class of

measuring instruments)

Not yet investigated

Freedom from bias Not yet investigated

Repeatability The prototype provides the same value for the same conditions of

measurement

6 Summary and conclusions

In software engineering, the analysis of software measures is usually discussed

from the perspective of measurement theory. We have proposed an approach here for

the analysis of some aspects of the strengths of software measures based on our mod-

eling of the set of metrology concepts documented in the ISO International vocabu-

lary of basic and general metrology terms (VIM). This was illustrated using one spe-

cific FSM method recognized as an ISO standard: COSMIC-FFP (ISO 19761).

The paper has documented the metrology concepts addressed in this ISO standard,

either in the design of this measurement method or in some of its practical uses. In

summary, it was observed that:

• On the one hand, the design of the COSMIC-FFP method covers a major-

ity of the metrology concepts described in the VIM dealing with the de-

sign of measurement methods;

• On the other hand, much larger-scale case studies will be required for the

study of the characteristics of measurement instruments as identified in

the VIM.

Measurement is recognized as a fundamental concept in engineering and provides

the information required to make key project decisions and take appropriate action. A

very large number of software measures has been proposed to industry to describe the

various characteristics of software in a quantitative manner, and much work remains

to be done in the study of both the design of software measurement methods and the

characteristics of measuring instruments for software measurement instrumentation in

industry.

Indeed, most of the metrology concepts related to measuring instruments still have

to be adequately explored by software engineers. It is suggested that the full set of

metrology concepts documented in the VIM be used as criteria to analyze the

strengths of other software FSM methods, as well as of other software measures sug-

gested to industry.

References

1. A. Abran, J. M. Desharnais, S. Oligny, D. St-Pierre, and C. Symons, "COSMIC

FFP Measurement Manual - Version 2.2, The COSMIC Implementation Guide for

ISO/IEC 19761: 2003," École de technologie supérieure – ETS, Montreal (Can-

ada) 2003. Available free at: www.lrgl.uqam.ca/cosmic-ffp

2. A. Abran and A. Sellami, "Initial Modeling of the Measurement Concepts in the

ISO Vocabulary of Terms in Metrology", 12th International Workshop on Soft-

ware Measurement – IWSM, Magdeburg (Germany) Oct. 7-9 2002, in Software

Measurement and Estimation, Shaker-Verlag, Aachen, 2002.

3. A. Abran, A. Sellami, and W. Suryn, "Metrology, measurement and metrics in

software engineering," Ninth International Software Metrics Symposium –

METRICS 2003, Sept. 3-5 2003, Sydney, Australia, IEEE Computer Society

Press, Los Alamitos, 2003.

4. S. Azzouz and A. Abran, "A proposed measurement role in the Rational Unified

Process (RUP) and its implementation with ISO 19761: COSMIC FFP," Software

Measurement European Forum SMEF 2004, Rome, Italy, Jan. 28-30, 2004.

5. N. E. Fenton and S. L. Pfleeger, Software Metrics: A Rigorous and Practical Ap-

proach: 2nd ed., PWS Publishing Co., 1997.

6. M. Hitz and B. Montazeri, "Chidamber and Kemerer's Metrics Suite: A Measure-

ment Theory Perspective," IEEE Transactions on Software Engineering, vol. 22,

pp. 267 -271, 1996.

7. ISO, International Vocabulary of Basic and General Terms in Metrology. Interna-

tional Organization for Standardization – ISO, Geneva, 1993.

8. ISO, ISO/IEC 9126-1 to 3: 2001, Information Technology – Software Quality

Characteristics and Metrics; Part 1: Quality model; Part 2: External metrics; Part

3: Internal metrics, International Organization for Standardization – ISO, Geneva

2001 to 2003.

9. ISO ISO/IEC 14143-1: 1998, Information technology -- Software measurement --

Functional size measurement -- Part 1: Definition of concepts, International Or-

ganization for Standardization – ISO, Geneva, 1998.

10. ISO ISO/IEC 19761: 2003, Software Engineering – COSMIC-FFP – A Functional

Size Measurement Method, International Organization for Standardization – ISO,

Geneva, 2003.

11. Zuse H., A Framework for Software Measurement, Walter de Gruyter, Germany,

Berlin, 1997.

Appendix A

The 6 categories of metrology concepts described in the ISO vocabulary of me-

trology [5] are:

1. Quantities and units: Table A.1

2. Measurements: Fig. A.1 and Fig. A.2

3. Measurement results: Table A.2

4. Measuring instruments: Fig. A.3, A.4, A.5, A.6 and A.7

5. Characteristics of the measuring instruments: Table A.3

6. Measurement standards – Etalon: Table A.4

A subset of the Tables and Figures from [8] are presented next.

Table A.1. Detailed topology of the Quantities and Units set of concepts

(Measurable) Quantity

Systems of

quantities

Dimension of a

quantity

Unit (of measurement) Value (of a quan-

tity)

Base quantity

Derived quantity

Quantity of

dimension one/

Dimensionless

quantity

Symbol of a unit

System of units

Coherent (derived) unit

Coherent system of units

International system of units

Base unit

Derived unit

Off-system unit

Multiple of a unit

Submultiple of a unit

True value

Conventional true

value

Numerical value

Conventional refer-

ence scale/Refer-

ence-value scale

Table A.2. Detailed topology of Measurement Results vocabulary

Result of a Measurement

Types of measurement

results

Modes of verification of

measurement results

Uncertainty of measurement

Indication Uncorrected

result

Corrected result

Accuracy of measurement

Repeatability

Reproducibility

Experimental standard deviation

Error (of measurement)

Deviation

Relative error

Random error

Systematic error

Correction

Correction factor

Table A.3. Detailed topology of the Characteristics of Measuring Instruments

Functionality test Quantitative Qualitative

Use Control

Measuring

Range

Rated operating condi-

tions

Limiting conditions

Reference conditions

Instrument constant

Response characteristic

Sensitivity

Discrimination

Resolution

Dead band

Stability

Transparency

Drift

Response time

Accuracy of a

measuring instru-

ment

Accuracy class

Freedom from bias

Repeatability

Error (of

indication)

Maximum

permissible

errors/ Limits

of permissible

error

Bias

Fiducial error

Datum

error

Zero error

Intrinsic

error

Nominal

Range

Span

Nominal

Value

Table A.4. Detailed topology of Measurement Standards / Etalons

(Measurement) Standard Etalon Conservation of a (Measurement) Standard

International (Measurement) Standard

National (Measurement) Standard

Primary Standard

Secondary Standard

Reference Standard

Working Standard

Transfer Standard

Traveling Standard

Traceability

Calibration

Reference Material (RM)

Certified Reference Material (CRM)

Metrology

Principle of Measurement

Method of Measurement

Measurement

Science of Measurement

Scientific Basis of a Measurement

Logical Sequence of Operations

Set of Operations

Fig. A.1. Measurement Foundations – High-level topology

Measurement Procedure

Measurand

Result of a

Measurement

Signal

Transformed

Value

Operator

Measurement

Method

Influence

Quantity

Fig. A.2. Measurement Process – Detailed topology of sub-concepts

Measuring

System

Stimulus

(Input Signal)

Response

(Output Signal)

Measuring Chain

Fig. A.3. High-level topology of Measuring Instruments

Measuring

Transducer

Measuring

Instrument

Correspondance

Read

Response

Measuring System

Material

Measure

Detector /

Sensor

Stimulus

Fig. A.4. Detailed topology of a Measuring System

Measurand

Another Quantity

Measuring

Instrument

Integrating

Instrument

Response

Fig. A.5. Integrating Instrument

and/or

Displaying (A/D) / Indicating (A/D)

Displaying Device / Indicating Device

Index

Recording (measuring) instrument

Rcording Device

Integrating

Measuring Instrument

Fig. A.6. Details of a Measuring Instrument

Scale

(set of marks)

Scale type Scale Division

Range of

indication

Scale spacing Scale Interval

Scale Numbering

Scale length

- Linear scale

- Nonlinear scale

- Suppressed-zero

scale

- Expanded scale

- Dial

Fig. A.7. Set of concepts related to scale