Rayleigh model

Anna University, Final CSE, Software Quality Management

1. Software Quality Management
Unit 
–
3 
Roy Antony Arnold G
AsstProf/CSE Asst
. 
Prof
.
/CSE

2. •
Software
reliability
models
are
•
Software
reliability
models
are
whenitisavailabletothe
customers.
•The criterion variable under stud
y
 is the number of 
y
defects in specified time intervals (weeks, months, 
etc.), or the time between failures. •Suchanestimateisimportantfortworeasons:
–(1) It is anobjective objective statement statementof thequality quality ofof thethe
dt dt
pro
d
uc
t
pro
d
uc
t
–(2) It is aresource planning toolfor thesoftware
maintenance
phase
maintenance
phase
.

4. •
Reliability
models
can
be
broadly
classified
into
two
categories
:
Reliability
models
can
be
broadly
classified
into
two
categories
:
and
(Conteetal.,1986).
•Astaticmodelusesother attributes of the project or program
modules
to
estimate
the
number
of
defects
in
the
software
modules
to
estimate
the
number
of
defects
in
the
software
.
GeneralForm:
Thenumberofdefects(y)isdependantontheattributes(x)ofthe The
 number
 of
 defects
 (y)
 is
 dependant
 on
 the
 attributes
 (x)
 of
 the
 
product and the process by which it is produced,  plus some 
error (e) due to unknowns which inherently exist.
•
A
dynamic
model
usually
based
on
statistical
distributions
uses
A
dynamic
model
,
usually
based
on
statistical
distributions
,
uses
thecurrent development defect patterns to estimate end‐
productreliability.
•
Dynamic
Models
are
classified
in
two
categories
Dynamic
Models
are
classified
in
two
categories
–those that model the entire development process (Rayleigh Model)
–those that model the back‐end testing phase (Exponential Model 
andReliabilityGrowthModels) and
 Reliability
 Growth
 Models)

5. •
The
Rayleigh
model
is
a
parametric
model
•
The
Rayleigh
model
is
a
parametric
model
inthesensethatitisbasedonaspecific
iil
di ib i
i
di
stat
ist
ica
l
di
str
ib
ut
ion.It
isa
d
ynam
ic
reliabilitymodel.
•When the parameters of the statistical
distribution
are
estimated
based
on
the
distribution
are
estimated
based
on
the
data from a software project, projections
bt
th
df t
t
f
th
jt
b
a
b
ou
t
th
e
d
e
f
ec
t
ra
t
eo
f
th
epro
j
ec
t
can
b
e
madebasedonthemodel.

6. •
The
Rayleigh
model
is
a
member
of
the
family
of
the
•
The
Rayleigh
model
is
a
member
of
the
family
of
the
.
•
One
of
its
marked
characteristics
is
that
the
tail
of
its
One
of
its
marked
characteristics
is
that
the
tail
of
its
probability density function approaches zero
asymptotically,butneverreachesit. •Weibulldistributions areused for predicting reliability and 
probability distribution
•Two standard functions for graphing Weibull

7. •
Rayleighisaspecialcaseofthe
Weibull
Rayleigh
 is
 a
 special
 case
 of
 the
 Weibull
where the shape parameter (m) equals 2:
•The formulas represent a standard distribution. •The total area under the curve is 
1
.
7

8. ¾Thedefectrateobserveddurin
g
thedevelo
p
ment
p
rocessis
g
p
p
positivelycorrelatedwiththedefectrateinthefield.(Fig.)
¾Assuming the defect removaleffectiveness remainsunchanged, then
hh
(
df )
d
dl
hh
a
h
ig
h
er curve
(
more
d
e
f
ects
)
d
uring
d
eve
lopment means a
h
ig
h
er
defectinjectionrateandhenceahigherfielddefectrate.
8

9. ¾
Given
the
same
error
injection
rate
if
more
defects
are
¾
Given
the
same
error
injection
rate
,
if
more
defects
are
discovered and removed earlier then fewer will remain in
latersta
g
esandthefield
q
ualit
y
willbebetter.
g
qy
–In the fig. the areas under the curves are the same but the curves 
peak at varying points. Curves that peak earlier have smaller areas 
at
thetail
theGAphase
at
 the
 tail
, 
the
 GA
 phase
.
In
short
“Do
it
right
the
first
time
”
In
short
,
“Do
it
right
the
first
time
.”
Thismeansthatifeachstepofthe development
process
is
executed
properly
development
process
is
executed
properly
with minimum errors, the end product's
qualitywillbegood.

10. ¾
Given
the
same
error
injection
rate
if
more
defects
are
¾
Given
the
same
error
injection
rate
,
if
more
defects
are
discovered and removed earlier then fewer will remain in
latersta
g
esandthefield
q
ualit
y
willbebetter.
g
qy
–In the fig. the areas under the curves are the same but the curves 
peak at varying points. Curves that peak earlier have smaller areas 
at
thetail
theGAphase
at
 the
 tail
, 
the
 GA
 phase
.

11. •
Most
statisticalsoftwarepackages
support
Most
 statistical
 software
 packages
 support
 
WeibullDistributions.
lbdlddh
•App
lications can 
b
e 
d
eve
lope
d
 d
ue to t
h
e 
clearly defined algorithms for Weibull.
•COTS (Commercial Off The Shelf) products 
canalsobeused: can
 also
 be
 used:
11

12. •
Accuracy
of
model
estimates
Accuracy
of
model
estimates
.
•Inputdatamustbeaccurateandreliable.
•
To
establish
high
Predictive
Validity,
To
establish
high
Predictive
Validity,
and empirical validity must be
established established
.
•Thevalidityofsoftwarereliabilitymodels
A
certain
model
may
work
well
for
a
.
A
certain
model
may
work
well
for
a
specificorganizationordevelopmentstructure,but
notforothers. •No universally
good software reliability model
exists.
12

13. •Hi
g
h‐level Desi
g
n Review 
(
I0
),
 Low‐level Desi
g
n Review 
(
I1
),
 Code 
g
g
(),
g
(),
Inspection (I2), Unit Test (UT), Component Test (CT), System Test (ST), 
and General Availability Phase (GA)