2
Chapter 1
6-is a scale parameter for infiaite sample size
fl-is a shape parameter for infinite sample size
y-is a threshold parameter
The computer solves for the Weibull parameters as well as the
Gaussian mean and standard deviation for a set of individual values from
mechanical testing or published bar charts with more than one or two
samples at a given value for the mid point of the bar (cell width).
Some computer software solves for only two Weibull parameters 6 and
/? while 7 is set to zero. The failure curvesf(x) and g(x) are used to generate
the reliability
F(x) = 1 - f(x)dx
(1.3)
G(x) = 1 - g(x)dx
(1.4)
The Weibull a(x), g(x) and Gaussian F(x)f(x) are unity curves with values
from zero to one. The Weibull and Gaussian curves are used throughout
this book except in chapter four where the constant failure-rate
for
reliability is introduced to explain the wear and tear on machinery. The
computer calculations for Eqs. (1.1) and (1.2) allows the individual
to be sorted or listed as a bar chart. Sturges Rule [1.12,1.16] presents an
acceptable means of plotting data on linear coordinates, where, the data
is grouped in cells of width w, over the range R, of the data.
1. Number of cells (K) = 1 + 3.3 logm N where N is the number of individual data points. Grouped data from bar charts are already
partitioned as presented in the data source, so the steps outlined
for using Sturges Rule will not apply: however, the number of cells
can be checked.
2. Range (R)= maximum value minus the minimum value.
3. Cell width (W)=R/K.
The number of cells can be rounded off, say -7.2 is 7 cells and -7.8 is 8
cells. Then using a sorted list of values partition the data into the number of
cells and plot N,- for each cell versus the value of the data in the center of a
cell width.
The test sample Gaussian curve values are calculated for the middle of
each cell width xi so from Eq. (1.1).
1
[ 1 [X i -- ~,~2"]
fi(xi)
= ~expL-5 ~-- ) J
(1.5)
If there are 8 cells the total is scaled up to reflect the total number of test
Chapter 1
6-is a scale parameter for infiaite sample size
fl-is a shape parameter for infinite sample size
y-is a threshold parameter
The computer solves for the Weibull parameters as well as the
Gaussian mean and standard deviation for a set of individual values from
mechanical testing or published bar charts with more than one or two
samples at a given value for the mid point of the bar (cell width).
Some computer software solves for only two Weibull parameters 6 and
/? while 7 is set to zero. The failure curvesf(x) and g(x) are used to generate
the reliability
F(x) = 1 - f(x)dx
(1.3)
G(x) = 1 - g(x)dx
(1.4)
The Weibull a(x), g(x) and Gaussian F(x)f(x) are unity curves with values
from zero to one. The Weibull and Gaussian curves are used throughout
this book except in chapter four where the constant failure-rate
for
reliability is introduced to explain the wear and tear on machinery. The
computer calculations for Eqs. (1.1) and (1.2) allows the individual
to be sorted or listed as a bar chart. Sturges Rule [1.12,1.16] presents an
acceptable means of plotting data on linear coordinates, where, the data
is grouped in cells of width w, over the range R, of the data.
1. Number of cells (K) = 1 + 3.3 logm N where N is the number of individual data points. Grouped data from bar charts are already
partitioned as presented in the data source, so the steps outlined
for using Sturges Rule will not apply: however, the number of cells
can be checked.
2. Range (R)= maximum value minus the minimum value.
3. Cell width (W)=R/K.
The number of cells can be rounded off, say -7.2 is 7 cells and -7.8 is 8
cells. Then using a sorted list of values partition the data into the number of
cells and plot N,- for each cell versus the value of the data in the center of a
cell width.
The test sample Gaussian curve values are calculated for the middle of
each cell width xi so from Eq. (1.1).
1
[ 1 [X i -- ~,~2"]
fi(xi)
= ~expL-5 ~-- ) J
(1.5)
If there are 8 cells the total is scaled up to reflect the total number of test