Quantitative Measurements of Maintainability I

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Quantitative Measurements of Maintainability I

• CPRE 416-Software Evolution and
  Maintenance-Lecture 5

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Contents

• Introduction and history of software measurements
• Defect Density (DD) Measure
• Critical analysis of the DD measure

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Introduction

• In software literature the terms metrics and
  measures are used as synonyms.
• More than 1000 software measures have been
  published measures based on size, complexity,
  quality, etc.
• Two famous measures created in seventies McCabe
  Measure and Halstead measure.
• Several investigations funded by federal
  agencies Rome Air Development Center (RADC),
  NASA.
• European Project METK 93 METKIT - Metrics
  Educational Toolkit. Information and Software
  Technology, Volume 35, No. 2, February 1993.

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Resources

• Good resources
• http//irb.cs.tu-berlin.de/zuse/metrics/History_0
  8.html
• http//www.sei.cmu.edu/str/descriptions/
• Earliest paper on software complexity Rubey,
  R.J. Hartwick, R.D. Quantitative Measurement
  Program Quality. ACM, National Computer
  Conference pp. 671-677, 1968.
• Bibliography http//irb.cs.uni-magdeburg.de/sw-en
  g/us/bibliography/bib_main.shtml
• Books
• Fenton, Software Metrics A Rigorous Approach.
• Grady, Software Metrics Establishing a
  Company-wide Program.
• Putnam and Myers, Five Core Metrics The
  Intelligence Behind Successful Software
  Management.

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Need for Software Measures

• The cost of software magnifies the need for
  quantitative analysis.
• Maintenance applications
• Predict error-proneness
• Predict the degree of maintainability
• Predict the difficulty of testing
• Other applications
• Cost estimates
• Track progress
• Determine relative complexity
• Validate best practices
• Measure productivity of programmers

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What we will study next

• We will study a few software measures.
• The specific measures may or may not be relevant
  to you in future.
• Our study will focus on
• Analyzing a measure and judging its
  applicability.
• Abstracting from concrete examples to develop
  useful insights about software measures.
• Principles of measurement.

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Critical Analysis of Measures

• Think about
• Is a given measure appropriate for your purpose?
  (e.g. Is LOC a good measure if my job is to fix a
  given set of defects?)
• Measures such as length, temperature etc. have
  certain intuitive properties that we are familiar
  with. These properties may not hold for a
  software measure.

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Defect Density (DD) Measure

• Lines of Code (LOC) and DD are widely used
  measures in industry.
• There are now companies that analyze your code
  for a given types of defects. Charges are based
  on LOC.
• Let us explore the DD measure.
• Definition DD Defects LOC

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Application In Practice

• We need two numbers LOC and defects.
• Many considerations may be needed in practice for
  counting defects.
• Typically, the number refers to defects found in
  a specified time interval.
• Many empirical studies and guidelines for
  applying software measures, for example
• http//www.dcs.qmul.ac.uk/norman/papers/qa_metric
  s_article/section_4_framework.html

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Question

• Suppose we have two versions of software V1 and
  V2.
• Both versions have n components.
• DD of each component of V1 is lower than the DD
  of the corresponding component of V2.
• Question Is the overall DD of V1 lower than that
  of V2?

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An Example
Source http//irb.cs.tu-berlin.de/zuse/metrics/l
ecture02.html (by Zuse)
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Discussion

• Mathematically, the example is about
• Given
• pairs of numbers (Ai, Bi) and (Xi, Yi)
• ( Ai / Bi ) lt ( Xi / Yi ) for i 1, 2, .. n.
• It does not imply that
• ( Sum(Ai)/ Sum(Bi)) lt ( Sum(Xi)/ Sum(Yi))

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Additive Measures

• Theory of Measurement defines the so called
  additive measures. The example shows that the DD
  is not an additive measure.
• Given a software engineering measure, always ask
  the question if it is an additive measure or not.

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What is a measure?

• A measure can be thought of as a relation
  preserving mapping (called homomorphism in
  mathematics)
• A software measure M maps software to real
  numbers. Given software S, M(S) is a real number
  called the measure of S.
• M preserves the relation . S1 S2 implies that
  M(S1) M(S2).

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Additive Property

• First, there is a notion of composing multiple
  pieces of software.
• Composition S1 o S2 (associative)
• A Measure is said to be additive if
• M(S1 o S2) M(S1) M(S2)
• An additive measure is called a scale.

Note We have simplified the mathematical
definition of additive measure to save time.