SOFTWARE DESIGN FOR X - Software Design for Six-Sigma: A Roadmap for Excellence - page 366

TABLE 14.2 ( Continued )

Formula for
Hazard Function

Data and/or Estimation
Required

Limitations and
Constraints Model Name

Estimation of α
(failure rate at start of
first interval)
Estimation of
β (proportionality
constant of failure rate
over time)

Assumes no new
faults are introduced
in correction.
Rate of fault detection
decreases
exponentially across
time.

λ t b
t

Time of each failure
occurrence
b estimated by
n/ ln(t n + t i )from i =
1 to number of
detected failures n.

Software must be
operational.

Duane's model

Number faults
remaining at start of
ith test (R i )
Test effort of each test
(K i )
Total number of faults
found in each test (n i )
Probability of fault
detection in ith test
Probability of
correcting faults
without introducing
new ones

Software developed
incrementally.
Rate of fault detection
assumed constant
across time.
Some software
modules may have
different test effort
then others.

Brook's and
Motley's IBM
model

Binomial Model
Expected number
of failures =

R i
n i

q n i (1 −
q i ) R i − n i
Poisson model
Expected number
failures =
( R i φ i ) n i exp − R i φ i
n i !

Time of each failure
detection
Simultaneous solving
of a and b

Software is
operational.
Fault detection rate is
S shaped across time.

ab 2 texp − bt Yamada, Ohba, and

Osaki's
S-Shaped model

1
a

b
a

Total number faults
found during each
testing interval
The length of each
testing interval
Parameter estimation
of a and b

Failure rate can be
increasing,
decreasing, or
constant.

Weibull model MTTF =