4
Chapter 1
I1. WEIBULL EQUATION VARIATIONS
Equation (1.2) may also be stated for infinite sample size
g(x) = ~- [-~]/~-l exp [- (-~)
~ ]
(1.14)
Comparing Eqs. (1.2) and (1.14)
o~ = ~
(1.15)
Published Weibull parameters have fl which is the same for Eqs. (1.2)
and (1.14) but, will have either O or 6; and may have a value for ~
analyzed as if it is zero. Also Eq. (1.4) will
G(x) = 1 - exp
6
--- 1 - exp -
(1.16)
The distribution is called:
(a)
(b)
Two parameter Weibull when/3 and O or 6 given and ? equal zero
and computer calculated.
Three parameter Weibull the same/3 and O or 6 and ? is the lowest
data value or selected by the computer.
III. PLOTTING RAW TABULATED TEST DATA OR USING
PUBLISHED BAR CHARTS
A. Weibull
The value of ~ can be determined from the finite sample data and is smaller
than the minimum value.
The finite sample plotting is performed on Weibull paper which is a In
In versus In graph paper as discussed in Appendix A. The data is divided
into cells using Sturges Rule (Section 1.1).
Percent failures
pf = ~ x 100
(1.17)
are plotted at the end of each cell and a best fit straight line is drawn through
the data and/3 estimated. The Weibull form for the line is
=l-exp -, e, /
~
(1.18)