Building a Composite Function in the Weibull++
Function Wizard
The Function Wizard in
Weibull++ allows
you to use
both math functions, which are functions such as cosines
or logarithms commonly found in spreadsheet software
packages, and data source functions, which are functions
such as reliability or failure rate that are based on data contained in
a Weibull++ data sheet. In addition, the Function
Wizard allows you to build composite functions by
combining any number of math and/or data source
functions into a single equation. This article will
provide an example of building a composite function
using the Weibull++ Function Wizard.
Consider a situation where a reliability engineer
wants to create a beta vs. B10 contour plot. To do this,
he computes a likelihood value using the following expression:
where
 is
the maximum likelihood value of a data set and
 is the
Chi-Squared statistic with a
significance level of
α and 2 degrees of freedom. This
expression requires both a data source function to
obtain the maximum likelihood value and a math function
to obtain the Chi-Squared statistic. Figure 1 shows the
engineer's data set, along with calculated parameters.
Figure 1 - Joe's
example data set
The above expression must be calculated in a General
Spreadsheet, which can be inserted by choosing Folio >
Insert General Spreadsheet or pressing CTRL+G. Figure 2 shows a
General
Spreadsheet with labels
entered in column A and the desired confidence level
entered in cell
B1. In addition, cell B2 (the position where the
expression will be inserted) is highlighted.
Figure 2 - The General Spreadsheet
before inserting
the calculated expression
The next step is to open the Function Wizard. You can
choose Data > Function Wizard or click the
icon.
The maximum likelihood value can be obtained using
the LK Value data source function, which returns the
maximum log-likelihood value. In order to obtain the
maximum likelihood value, we will need to use the
following fact:
This expression can be built in the Function Wizard
using the following steps:
- In the drop-down list at the top left, choose
All functions.
- In the list of functions on the left, choose the
EXP function. The area on the right will
display the inputs for the selected function.
- In the Number text box, enter 1
and click the Add to Equation button. EXP(1) will
appear in the Composite Function area at the bottom of the
Function Wizard, as shown in Figure 3.
Figure 3 - The Function Wizard
after inserting the
first function
- Select the number 1 (i.e., the argument of the EXP
function) in the Composite Function area, as shown in
Figure 4.
Figure 4 - Selecting the argument of the EXP function
- In the Function List, choose the LKVALUE function.
- Press the Select button in the Data
Source field and choose
the data sheet. Click the Add to Equation button. The
Composite Function area will look like the one shown in Figure
5.
Figure
5 - The Function Wizard after creating the
expression for the maximum likelihood value
The second half of the expression for the likelihood
value can be built in the Function Wizard as follows:
- At the end of the expression
in the Composite Function area, enter a multiplication
sign (*). Then insert
another EXP function as shown above.
- Select the argument of the second
EXP function (i.e., 1) in the Composite Function area,
as shown in Figure 6.
Figure 6 - Selecting the argument of the second EXP
function
- In the Function List, choose the CHIINV function.
- Enter 1 in the Probability text box and enter
2 in the Degr_Freedom text box, which
allows you to specify the degrees of freedom.
Click
the Add to Equation button. The Composite
Function area will look like the one shown in Figure
7.
Figure
7
- The Function Wizard after inserting the functions needed to
build the Chi-Squared statistic
- Immediately before the CHIINV function in
the Composite Function area, enter a minus sign (-),
as indicated by the arrow in Figure 8.
Figure 8 - Entering the minus sign for the CHIINV
function
- Immediately after the number 1 (i.e., the first
argument of the CHIINV function) in the Composite
Function area, type -B1/100. This is underlined
in red in Figure 9. (The expression
1-B1/100 is used to convert the confidence level in cell
B1 to the significance level required by the CHIINV
function.)
Figure 9 - Completing the -B1/100 expression
- Immediately before the
last parenthesis, type /2. The Composite
Function area will look like the one shown in Figure 10.
Figure
10 - The Function Wizard containing
the entire likelihood expression
- The final step is to
click Insert. The Function Wizard will be closed
and the
calculated expression will appear in cell B2, as shown in
Figure 11.
Figure
11 - The General
Spreadsheet after inserting the calculated expression
As demonstrated in this article, the Composite Function
area of the Function Wizard allows you to build
functions containing more than one math and/or data
source function. This eliminates the need to use
multiple cells of a General Spreadsheet for these types
of calculations. This feature also works when building
custom reports in Weibull++ using the Reports
utility.
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