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4.1 Experimental Setting in Statistical Method
Prior to migrate towards the Machine Learning approach, a brief estimation of
statistical parameter of reliability measure could be accumulated. Hence, both
NHPP and Newton Raphson model is envisaged.
4.1.1 Parameter Estimation
The software failure process is modeled by NHPP model with mean value function
given as:
e
bt
a and b other parameters to be estimated from the
failure data (the parameter is interpreted as the number of initial faults in the
software and the parameter b is the fault detection rate which is related to the
reliability growth rate in the testing process.
Once the model has been constructed, its parameters a and b can be estimated
using maximum-likelihood estimation technique. The parameter b can be deter-
mined numerically using a technique known as Newton-Raphson. Newton-Raphson
method is one of the most popularly used numerical techniques for solving complex
non-linear equations which has good convergence. It is a method for
l
ð
t
Þ¼
a
ð
1
Þ
finding suc-
cessively better linear approximations to the roots (or zeroes) of a real-valued
function. The idea of the method is as follows: one starts with an initial guess which
is reasonably close to the true root, then the function is approximated by its tangent
line (which can be computed using the tools of calculus), and one computes the x-
intercept of this tangent line (which is easily done with elementary algebra). This x-
intercept will typically be a better approximation to the function
'
s root than the
original guess, and the method can be iterated. Given a function f over the real
values of x and its derivative f, the method begins with a first guess x0 for a root of
the function f. Then the better approximation of the root is calculated as follows:
x
o
Þ
f
0
ð
x
o
Þ
f
ð
x
1
¼
x
0
ð
1
Þ
The process is repeated as:
ð
Þ
f
n
x
n
þ
1
¼
x
n
ð
2
Þ
f
0
ð
x
n
Þ
until a suf
ciently accurate value is reached.
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