How to calculate the signal-to-noise ratios and the standard deviations in the response table for Taguchi design

The Response Table for SIgnal-to-Noise Ratios contains a row for the average signal-to-noise ratio for each factor level, Delta, and Rank. The table contains a column for each factor.

The Response Table for Standard Deviations contains a row for the average signal-to-noise ratio for each factor level, Delta, and Rank. The table contains a column for each factor.

Delta
Delta is the difference between the maximum and minimum average response (signal-to-noise ratio or standard deviation) for the factor.
Rank
The Rank is the rank of each Delta, where Rank 1 is the largest Delta.

Calculate the signal-to-noise ratios

To get the standard deviation for each factor level, consider the following example. You have a Taguchi design where the inner array has 2 factors (A and B), stored in C1 and C2, respectively, and the outer array has two responses, stored in C3 and C4.

Part 1

  1. Choose Calc > Row Statistics.
  2. Choose Mean.
  3. In Input variables, enter C3 C4.
  4. In Store result in, enter C6.
  5. Click OK.

Part 2

  1. Choose Calc > Row Statistics.
  2. Choose Standard deviation.
  3. In Input variables, enter C3 C4.
  4. In Store result in, enter C7.
  5. Click OK.

Part 3

  1. Choose Calc > Calculator.
  2. In Store result in variable, enter C8.
  3. In Expression, enter: 10 * LOGT(C6**2 / C7**2).
  4. Click OK.
Note

You can also get these signal-to-noise ratios by choosing Stat > DOE > Taguchi > Analyze Taguchi Design, clicking Storage, checking Signal to Noise ratios, and clicking OK twice.

Part 4

  1. Choose Stat > Basic Statistics > Store Descriptive Statistics > Statistics.
  2. In Variables, enter C8.
  3. In By variables (optional), enter C1.
  4. Click Statistics.
  5. Check Mean.
  6. Click OK twice.

The last column in the worksheet (named Mean1 if there was not already a column with this name before performing these steps) contains the signal-to-noise ratios that are displayed in the Response Table for factor A.

Repeat Part 4, entering C2 in step 3 to get the signal-to-noise ratios for factor B.

Calculate the standard deviations

To get the standard deviation for each factor level, consider the following example. You have a Taguchi design where the inner array has 2 factors (A and B), stored in C1 and C2, respectively, and the outer array has two responses, stored in C3 and C4.

Part 1

  1. Choose Calc > Row Statistics.
  2. Choose Standard deviation.
  3. In Input variables, enter C3 C4.
  4. In Store result in, enter C6.
  5. Click OK.
Note

You can also get these standard deviations by choosing Stat > DOE > Taguchi > Analyze Taguchi Design, clicking Storage, checking Standard deviations, and clicking OK twice.

Part 2

  1. Choose Stat > Basic Statistics > Store Descriptive Statistics > Statistics.
  2. In Variables, enter C6.
  3. In By variables (optional), enter C1.
  4. Click Statistics.
  5. Check Mean.
  6. Click OK twice.

The last column in the worksheet (named Mean1 if there was not already a column with this name before performing these steps) contains the standard deviations that are displayed in the Response Table for factor A.

Repeat Part 2, entering C2 in step 3 to get the standard deviations for factor B.

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