Remaining Life of a Pipeline

Estimation of the pdf (E(t)) (using Mathcad 5)
Initial approximation for "thickness reduction rate": υ 0.00001
Initial approximation for standar deviation:.σ 0.007
Initial Wall Thicness: Eo 0.23
ln
1
2. π . σ
2
1 E Eo.
e υ .
. t
ln(likelihood) function
2 σ
( E Eo.
exp( υ . t)
) . exp( υ . t)
σ 2
( E Eo.
exp( υ . t)
) . Eo. t . exp( υ . t)
d(ln(likelihood))/d υ
σ 2
1 ( E Eo.
exp( υ . t)
) 2
σ
σ 3
Given
d(ln(likelihood))/d σ
n
i = 0
n
i = 0
σ
1
2
E i
Eo. exp υ . t i
σ 3
E i
Eo.
exp υ . t i
σ 2
0
. Eo. t .
i
exp υ . t i
0
System of Equations
n
i = 0
E i
Eo.
exp υ . t i
. exp υ . t
σ 2 i
0
0.011
Sol Minerr( σ , υ,
Eo) Sol = 3.195 10 5 Solutions for "σ" y para " υ"
0.235
35