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# 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. 