Appendix A
Linearization of the WeibullEquation
The Weibull Equation Eq. (4.11) and [1.5]
d[ln R(t)]
f(t)
h(O - - -(A.1)
dt
1 - F(t)
Integrating
R(t) = exp - h(~)dr
(A.2)
if h(r) is Weibull from Eq. (1.2) and Eq. (1.16)
[ln R(t)] = - ~ (t - ~-I
(A.3)
dt
Integrating from V the lowest value of the data to t = z
In R(t) = - ~ (~ - 7)
1
(A.4)
_ (t - ~)~
This equation is a natural logarithmic form of the following in the two forms
Eq. (1.16) also called Q(t) the failure
Q(t)=l-exp
- ¯
(A.5)
Q(t) = 1 - exp
(A.6)
and also note h(t) is a constant
Q(t) = 1 - exp[-Xt]
(A.7)
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