Diversity and Multi-Version Systems - Nuclear Power Plant Instrumentation and Control Systems for Safety and Security - page 203

n 1 , n 2 - a number of errors in the first and the
second program-version, respectively.
In accordance with the formula, diversity in-
dicator β changes from 0 to 1 and takes on limit
values in the following cases:

statistical code analyzer; (2) calculation of abso-
lute value of remainder obtained from a pair of
each program-version metrics; (3) rating absolute
values of metrics obtained at stage 2; (4) deter-
mination of the diversity indicator β .
Further, values of diversity indicators, obtained
by using direct and indirect metrics, should be
compared to determine their correlation.
To assess proposed MVS assessment tech-
niques two-version projects were obtained in
programming languages С#, Java, C++. Only
versions of initial programs with errors were
assessed. Assessment results of two-version
projects are presented in Table 7. Each project is
a solution for one of the five tasks characterized
by complexity level, where I - the lowest level of
task complexity, III - the highest level (Duzhyi,
V., et al, 2010).
From the table it appears:

0 ,

,

if
if

n
n

=
=

0

com

β = .

1 n

err 1 err 2

Gain, obtained by the diversity, is ∆ = 1 β
If all errors match in both program-versions
( β =1), there will be no gain (Δ=0), because both
MVS versions will operate inaccurately. If errors
differ in each version (ideal case) ( β =0), majority
element will be able to determine different values
in each channel; so, in this case there will be the
largest gain (Δ=1). If diversity indicator is in
the range (0< β <1), obtained gain indicates that
in both versions a number of undetected errors
is decreased by value (Δ*100) percentagewise.
Indirect metrics-based assessment of the di-
versity indicator β of two-version design has the
following stages: (1) measurement of absolute
values of each program-version metrics, using

• Diversity allows increasing quality of most
projects.

• Subject diversity allows increasing proj-

ect quality independently of programming
language.

Table 7. Results of MVP experimental researches

Task Level of

Complexity

Language Number of

Projects (MVP)

β Gain by Diversity, %

by MVP

0 0...1 1

1 I C# 3 2 0 1 67

Java 91 16 61 14 85

C++ 465 99 343 23 95

2 II C# 21 0 21 0 100

Java 153 12 132 9 94

C++ 465 20 439 6 99

3 I C# 45 6 38 1 98

Java 45 0 38 7 84

C++ 435 64 323 48 89

4 II Java 3 2 1 0 100

C++ 231 0 211 20 91

5 III Java 3 0 3 0 100

C++ 10 4 6 0 100