Example 6 - Taguchi Orthogonal Array Design
Taguchi orthogonal array (OA) designs are often used in design experiments with multiple level factors. Taguchi OA can be thought of as a general fractional factorial design.
Consider an experiment to study the effect of four three-level factors on a fine gold wire bonding process in an IC chip-package.* Taguchi OA L27 (3^13) is applied to identify the critical parameters in the wire bonding process. The response is the ball size. The smaller the ball size, the better the process.
For this example, the four factors are:
These four factors are assigned to columns 1, 2, 5 and 8 in L27. The remaining columns either represent the interaction effects of these factors or are treated as dummy factors. For example, columns 3 and 4 are the interaction of AB. Columns 6 and 7 are the interaction of AE. Columns 9 and 10 represent the effect of AH. Those columns can be deleted from the design matrix and will not affect the analysis results. More detailed discussion on the properties of Taguchi arrays can be found in the appendix of Taguchi’s handbook.**
The experimenters use DOE++ to design a Taguchi OA design. The design-specific settings, the factor properties and the response properties used are shown next.
Once the Standard Folio has been created, all unused factor columns are deleted, keeping only the Force, Power, Time and Temperature columns in the design matrix. The Time column then becomes factor C and Temperature becomes factor D.
The design matrix and the response data are given in the "Taguchi OA L27(3^13)" Folio.
Analysis Part I
Step 1: After performing the experiment according to the design and recording the results, the experimenters enter the data set into the Standard Folio, as shown next.
Step 2: The following effects are selected for inclusion in the analysis:
Step 3: The data set is analyzed with the default risk (significance) level of 0.1, using individual terms. The ANOVA table from the Analysis tab is shown next.
This table shows that effects A, B and C are significant.
Analysis Part II
The results for the reduced model and the optimization are given in the "Reduced Model" Folio.
Step 1: The design Folio is duplicated and the copy is named "Reduced Model."
Step 2: Only the significant effects are selected to calculate the new model, as shown next.
Step 3: The reduced model is calculated.
Step 4: To identify which factor settings can provide the smallest ball size, the Diagnostics window is used, as shown next. The Fitted Value column is the expected ball size for the factor settings under different runs.
From the Fitted Value column, it is determined that run order 4 (standard order 1) gives the best result. The predicted ball size is 35.1667. The settings are Force = 5, Power = 40 and Time = 15.
In Taguchi OA Factorial design, all factors are assumed to be qualitative factors, which means that the factors can only take the discrete values defined in the design, which in this case are:
If the factors can be treated as quantitative factors, meaning they can take any value within a range, further analysis using response surface methodology should be conducted to find the optimal settings for the manufacturing process.
* T. Hou, S. Chen, T. Lin and K. Huang, "An integrated system for setting the optimal parameters in IC chip-package wire bonding process," Int. J Adv Manuf Technology, 2006, 30, 247-253.
** G. Taguchi, S. Chowdhury and Y. Wu, Taguchi's Quality Handbook, Hoboken, New Jersey, Wiley, 2004.