Data Reduction
3
data.
or
i=8
N = )~ ~-~f,’(xi)
(1.6)
i=1
N
)~ -- ~,~ ft.(Xi)
(1.7)
Equation (1.7) is a scaling factor which at each midpoint expands the
Gaussian unity curve-value f.(xi) to reflect the actual data so that
Z Ni = N
(1.8)
where N is the total number of test samples and is a check on the calculations.
The Weibull equation is also expanded and plotted on the same bar
chart with the Gaussian curve.
Equation (1.2) for the midpoints of the cells i is expressed
gi(xi) -- ~[Xi -- 7~]/~-1 exp
(1.9)
Then
N = Y Z gi(xi)
(1.10)
Solving for Y by summing on i
N
Y --(1.11)
which expands each midpoint of the Weibull plot so that
N = Y N~
(1.12)
Again a check on calculations is made.
The data may be further checked by plotting the sum of the failures
y foXg(x)dx= x foXf(x)dx Y~N~(1.13
Verus a log scale on the right hand side. This is done by adding from i-- 1 to
the desired cell, dividing by N and plotting this value at the end of cell i. This
is a probability of failure and when it is 0.5 it gives a good check on the
Gaussian mean and the peak of the Weibull curve. The value 0.5 is also
called a 50th percentile for the data and shows how the data is skewed.