**The Weibull Trending Toolkit (wtt01.exe) is year 2000
copyrighted property of:**

Glenn E. Bowie

2426 Hallquist Ave.

Red
Wing, MN 55066

(651) 388-2374

e-mail: glennbowie@hotmail.com
Use a display monitor with 800 x 600 resolution.

wtt01.EXE

SORT.BAS

MAKEFILE.BAS

6300.DAT

7075.DAT

wtt01.EXE runs on an IBM compatible PC with Microsoft Windows. It has
been tested on WINDOWS 3.1, 95 and 98 systems. Make sure you have
VBRUN300.DLL in your c:>WINDOWS\SYSTEM directory.

With a WIN 3.1 system, you can start with the C:>WTT01 prompt:
just type wtt01 and you will see the first interactive display.

The usual way to start the weibull trending toolkit program wtt01.exe
is to enter the program name, in this case wtt01, at the RUN command.

Click the "Match Sample Statistics" button.

Enter file name 6300,
then click button "OK".

Notice on the bottom line the UCL = 574.4.
Choose an upper graph limit greater than UCL. Try 800. Click "Plot
Control Chart" and enter 800

Click the upper left button in the graph display to see a menu. Click
Close. You have gone back to the first application screen. Click the
upper left button and Close once more to exit.

To go on, click "Match Sample Statistics" again. Enter filename 7075
Choose graph upper limit 80

About the files:

6300 and 7075 are from "A Reliability Analysis
Approach To Fatigue Life Variability Of Aircraft Sructures", by I. C.
Whittaker and P. M. Besuner, The Boeing Company, April 1969,
AFML-TR-69-65.

Item 6300 data are on p. 229. There are 102 fatigue lives for 6061-T6
Al specimens in the file. See p. 159 to compare with Boeing
two-parameter Weibull results.

7075 data are on p. 175, item 417. 31 failures of 7075-T6 bare
specimens. Two-parameters on p. 123.

Weibull Analysis Tips

Weibull analyses are restricted to positive magnitudes. The skewness
and kurtosis of a normal probability density distribution both equal
zero. Sample distributions of random noise rarely have zero skewness and
kurtosis. Stated different ly: random noise sample distributions are
usually non-normal. By design, program WTT makes the skewness of the
Weibull distribution have the same value as the skewness of the sample
distribution. Positive skewness means the sample and Weibull
distributions have relatively long tails in the direction of larger
values than the mode. Negative skewness means the tail toward values
less than the mode is relatively long. The mode is the most frequently
occurring value. A mode only exists for a Weibull distribution when
parameter k is greater than one.

A distribution with positive kurtosis has a relatively flatter peak
and longer tails than a normal distribution. Negative kurtosis means the
distribution is more peaked and has shorter tails than a normal
distribution.

Skewness of a Weibull distribution equals zero when parameter k
equals 3.60232. The skewness is positive when k is greater than this
value and is negative when it is less. This helps explain why k is
called the shape parameter. For a Weibull distribution, random \
magnitudes are greater than threshold parameter e. Threshold e must
never be less than zero. For all values of k greater than zero, 63.21%
of the random values described by a Weibull distribution are less than
or equal to characteristic value v and the remaining 36.79% are greater
than v.

Weibull 99.73% Probability Control Band

The graphs have the form of a SPC chart. Commercial Weibull analysis
programs often require that measurements be ordered from smallest to
largest in order to estimate Weibull parameters. Program WTT does not.

For a normal distribution, 99.73% of the random values are within a
band defined by distances measured from the mean equal to plus and minus
3 times the standard deviation. For a normal distribution, a 99.73%
probability band has a width of 6 times the standard deviation. Program
WTT determines upper and lower control limits UCL and LCL by means of
the three Weibull parameters. The percentage area under the Weibull
distribution between LCL and threshold e is equal to 0.135%, and the
percentage at greater values than UCL equals 0.135%.

__________________________________________________________________
BASIC SUBTOOLS

Type Qbasic SORT Look at the list. Suppose you have generated a
sequential file with name MY01.DAT. It begins with N the number of data
values in the file. Enter MY01 as a file NAME and it generates OMY01,
with the data values ordered from smallest to largest.

MAKEFILE.BAS can help you make a sequential data file.

All the best,

**Glenn E. Bowie**