A Metric Suite for Object Oriented Design by S' R' Chidamber and C' F' Kemerer 1994

1
A Metric Suite for Object Oriented Designby S.
R. Chidamber and C. F. Kemerer (1994)

• 2 criticisms of metrics during the early phase of
  OO.
• Complexity metrics lacked solid theoretical bases
  ( e.g. E. Weyuker)
• Traditional metrics do not include OO concepts
• The goal of the paper
• Propose metrics that have a firm basis in theory
• Evaluate the metrics against established criteria
  (e.g. Weyuker)
• Present empirical data to illustrate the
  characteristics of metrics

2
Boochs OO Design

• Theory behind OO Design centers around CLASS
• Identification of classes
• Defining the meaning of classes
• Defining the relationships between/among classes
• Defining the implementation of a class with
  methods and data
• Thus, metrics of OO design measure the complexity
  in designing CLASSES
• The metrics outlined here mainly captures static
  behavior, not dynamic behavior.

3
Measurement Theory

• OO design may be viewed more formally as a
  system, D, with 3 components
• Design, D ( C, R, B) where
• C set of classes
• R is a set of empirical relations on the classes,
  C.
• B is a set of binary operation on the elements of
  C.
• An example of empirical relationship is gt, where
  a class is gt another class if it contains more
  methods.
• Note that a binary relationship may have
  properties such as transitivity or completeness
  (every element participates)
• In order for the OO empirical system to be
  measured, it must be transformed into a formal
  system that has relations and operations. An
  example of such a formal system is the real
  number system, which is ordered. (Example with
  height of children)
• Childrens height
  ? real number
• Relation taller ?
  relation gt
• Binary op standing on top ? binary
  op
• This is a transformation metric, M, where for d
  in Design, D (C,R,B), is mapped to a formal
  real system, Real (n, R, Op)
• or M(d) ? Real

4
Some Important Concepts Definitions

• Each object, or element, in OO is an individual
  that has properties.
• Object is a representation of an application
  domain, as seen by the designer, that includes
• Methods
• Instance variables
• More formally, Object (i, P(i) ) where
• i individual object
• P(i) collection of properties of i
• For an individual object, x, the properties of x,
  P(x), are described with methods, (Mx) and
  instance variables, (IVx) .
• P(x) M x U IV x where U is the
  logical union, OR, of sets

5
Design Properties for OO

• Coupling in OO between two objects X and Y is
  defined as
• (1) action by Mx on P(y) My U IVy
  or
• (2) action by My on P(x) Mx U IVx
• 2. Cohesion is defined in terms of a similarity
  function, S, where
• S(A, B) P(A) P(B) , is the logical
  intersection, AND, of sets
• Consider M1 and M2, methods 1 and 2 of the same
  Object.
• S(M1, M2) IV1 IV2 where IV1 is the
  set of instance variables accessed by method M1.
• Cohesion is defined by this similarity function
  based on the belief that different methods of the
  same object performing different operations on
  the same set of instance variables implies that
  the object is cohesive. (The degree of similarity
  is based on the similarity of methods which in
  turn is measured by the number of the common
  instance variables.)

6
Design Properties for OO (cont.)

• 3. Complexity of an object may be viewed as
  the cardinality of the objects set of properties
  based on the concept that the larger the set of
  anything, the more complex it is. (properties may
  be anything of interest such as input
  variables)
• 4. Scope of properties of an object speaks
  to how far an objects properties influences
  other objects.
• In OO, the depth of inheritance may be viewed as
  the scope.
• Depth of Inheritance depth of class in the
  inheritance tree
• In OO, the number of children of a class may also
  be viewed as an influencing factor.
• Number of children of a class number of
  immediate descendants of a class
• 5. Communications among the methods is
  another measure of OO design this is like
  coupling
• Response set of a class of objects all
  methods that can be invoked in response to a
  message to an object of the class
• 6. Combination of objects, X and Y, is
  defined as the logical union of P(X) and P(Y).
  (not clear on the applicability of this in OO)

7
E. Weyukers 9 Metric Evaluation Criteria

• Let m be a metric for a program entity then it
  should have the following properties
• Non-Coarseness given any program X there is
  another program Y where m(X) ! m (Y)
• Non-Uniqueness there exist program entities
  X and Y such that m (X) m(Y)
• Permutation is significant there exists
  program entities X and Y such that X is a
  rearrangement of Y and m (x) ! m (Y)
• Implementation (design detail) is important
  there exists programs X and Y such that they
  produce the same output given the same input and
  m (X) ! m (Y)
• Monotonicity given program entities X, Y, m
  (X) lt m (X Y) and m (Y) lt m (X Y) where
  is the concatenation of X and Y.
• Non-equivalence of interaction there are
  program entities of X,Y, and Z such that m (X)
  m (Y) but m (X Z) ! m ( YZ)
• Interaction increases complexity there are
  program entities X, and Y such that m(X) m(Y)
  lt m (X Y) where the first is addition and
  second is some other operation such as
  concatenation.
• Finiteness given a nonnegative number, c,
  there is only a finite number of program entities
  that satisfies m(X) c.
• Renaming Principle if Y is a renaming of X,
  the m(X) m(Y)
• Are not considered by C-K in this article

8
6 C-K Metrics for OO design

• Weighted Methods per Class (WMC)
• WMC SUM( Cj ), where C1, ----, Cn are the
  complexity weights assigned to each of the
  methods M1, ----, Mn in the class.
• If the weights are all equal to 1, then WMC
  number of methods in the class.
• (based on the complexity property of larger the
  cardinality of a set of methods the more time and
  effort is needed.)
• Depth of Inheritance Tree (DIT)
• DIT length of a node to the root of an
  inheritance tree.
• In case of multiple inheritance, pick the maximum
  length.
• (based on the scoping property, where the deeper
  scope indicates more influence in depth that is
  harder to understand.)

9
6 C-K Metrics for OO design

• Number of Children (NOC)
• NOC number of immediate sub-classes subordinate
  to the class.
• (based on the scoping property where the broader
  the scope implies more influence in breadth and
  possibly more complexity.)
• Coupling Between Objects (CBO)
• CBO number of classes a class is coupled to,
  where coupled is defined as a method in a class
  calling another class or uses its variables.
• The notion of coupling allows for both fan-in and
  fan-out.
• (based on the coupling property where less
  coupling is better more coupling prevents re-use
  and is hard to maintain)

10
6 C-K Metrics for OO design

• Response for a class (RFC)
• RFC (number of methods in class) (number of
  remote methods called by the methods in class),
  the operator is the arithmetic sum.
• A called on method is counted once even if it may
  be called several times.
• (based on the complexity and communication
  properties where higher cardinality implies more
  difficulty more testing also)
• Lack of Cohesion in Methods (LCOM)
• LCOM (Cardinality of P) (Cardinality of Q)
  if cardinality of P is gt cardinality of Q
  otherwise LCOM 0, where
• For each method Mj, IVj set of instance
  variables used by Mj
• P (IVj, IVk) where logical intersection of
  IVj and IVk is empty
• Q (IVj, IVk) where logical intersection of
  IVj and IVk is non-empty
• (based on the idea that similarity of methods
  gives us cohesion and less similarity shows lack
  of cohesion --- where similarity of methods in a
  class is defined as operating on the same
  instance variable )

Note that degree of 0 is not included in LCOM
that is, no matter by how much the cardinality of
Q is bigger than cardinality of P, it is the same
zero!
11
Meeting OO Boochs Design Theory(Steps)

• Earlier it is said that the theory behind OO
  design centers around class
• Identification of classes
• Defining the meaning of classes
• Defining the relationships between/among classes
• Defining the implementation of a class with
  methods and data
• Do the C-K metrics cover all these design points
  of CLASS ?

12
C-K Metrics coverage of OO Design Steps
Do you agree with the authors assessment?
13
Meeting Weyukers Metric Evaluation ?
metric
W1
W2
W4
W5
W6
W7
WMC
Yes
Yes
Yes
Yes
Yes
No
DIT
Yes
Yes
Yes
No
Yes
No
NOC
Yes
Yes
Yes
Yes
Yes
No
CBO
Yes
Yes
Yes
Yes
Yes
No
RFC
Yes
Yes
Yes
Yes
Yes
No
LCOM
Yes
Yes
Yes
NO
Yes
No

• W7 is interaction increases complexity none
  of the metrics satisfy
• this condition
• W8-finiteness and W9-renamingapplies to all
  metrics W3-permutation is not applicable

14
Some Managerial Usage of these metrics

• Data from 2 commercial projects indicated that
  designers kept inheritance hierarchies shallow
  this indicates that for simplicity, the designers
  gave up some re-use. (Can managers encourage
  people to increase DIT or NOC ?)
• Another observation indicated that a class had a
  large number (42) of sub-classing. In this case,
  looking at NOC helped find some potential excess
  in sub-classing.
• Clearly, combinations of metrics may also help
  manage the over-all design.
• WMC along with NOC and DIT to look at structuring
  of class
• CBO and RFC to look at excessive interaction and
  communications