2.42.3.3.1 Interpreting Results for Analyze Design


Contents

Report Sheet

The tables in the section are included in the report sheet for analyze design, which is named DOEAnalysis

Coded Coefficients

DOE Analyze Design Coded Coeff Tbl.png

The coded coefficients table presents the regression coefficients using standardized (coded) factor levels, typically ranging from −1 to +1.

Coefficients

The estimated model coefficients (slopes) for each factor and interaction.

Standard Error

The precision of each coefficient estimate. Smaller values mean more reliable estimates.

Confidence Limits (95% LCL, 95% UCL)

The lower and upper bounds of the confidence interval for each coefficient, based on the chosen confidence level.

t-Value

The test statistic used to judge whether a coefficient is significantly different from zero.

Prob>|t|

The p-value associated with the t-test. Values below your significance threshold (commonly 0.05) indicate significant terms.

VIF

Variance Inflation Factor. Values much larger than 1 suggest multicollinearity among model terms.

Example

Term Coefficient Interpretation
A 3.12 Increasing factor A increases the response.
B -1.75 Increasing factor B decreases the response.
AB 2.05 Factors A and B interact significantly.

Regression Equation in Coded Units

The coded regression equation predicts the response using standardized factor levels.

Uncoded Coefficients

The uncoded coefficients are expressed using the actual experimental units.

Example:

Factor Coefficient
Temperature (°C) 0.42
Pressure (bar) -0.18

Regression Equation in Uncoded Units

Provides a prediction equation using actual operating conditions.

Statistics

R-Square

Represents the percentage of response variation explained by the model.

Adj. R-Square

Adjusted R-square, which accounts for the number of predictors in the model. It penalizes over-fitting and is the preferred metric when comparing models with different numbers of terms

PRESS

Predicted Residual Sum of Squares. A measure of how well the model predicts new observations, calculated by iteratively leaving out one observation at a time. Smaller is better.

Residual Sum of Square

Residual Sum of Square is actually the sum of the square of the vertical deviations from each data point to the fitting regression line. It can be inferred that your data is perfect fit if the value of RSS is equal to zero

Root-MSE (SD)

The square root of the mean square error. It estimates the standard deviation of the random error (noise) around the fitted model. Smaller is better.

Pred. R-Square

Predicted R-square. It estimates how well the model predicts future observations. A value close to the R-square indicates the model is not over-fitted and will generalize well

AIC

Akaike Information Criterion. It evaluates model fit while penalizing model complexity. When comparing models fitted to the same data, a smaller AIC generally indicates a better balance between fit and complexity.

AICc

Corrected Akaike Information Criterion. It applies an additional correction to AIC for smaller sample sizes. As with AIC, smaller values indicate a preferable model when comparing models fitted to the same data

BIC

Bayesian Information Criterion. Like AIC, BIC balances model fit and complexity, but applies a stronger penalty for additional model terms. A smaller BIC generally indicates a better model when comparing competing models.

ANOVA

DOE Analyze Design ANOVA.png

The ANOVA (Analysis of Variance) table tests whether each term contributes significantly to explaining the response.


Lack of Fit

The Lack of Fit test is used to determine whether the selected model adequately describes the relationship between the factors and the response.

The test separates the model error into two components:

  • Lack of Fit
  • Pure Error

The Lack of Fit Test compares these two sources of variation using an F-test:

\[ F = \frac{\text{Mean Square of Lack of Fit}}{\text{Mean Square of Pure Error}} \]


The test results are in the ANOVA table of report sheet.

DOE Analyze Design Lack of fit.png

Lack of Fit

Variation indicating that the model does not adequately capture the true relationship between the factors and the response

A small p-value indicates significant lack of fit

  • P > 0.05: The model fits the data adequately
  • P < 0.05: Indicates significant lack of fit, suggesting that the model may be inadequate and that a different model or additional terms may be needed.

Pure Error

Variation caused by random experimental error, estimated from replicated experimental runs.

Means Table

DOE Analyze Design Means Tbl.png

The means table shows the average response at each factor level.

Response Table

DOE Analyze Design Taguchi Response Tbl.png

The response tables, available for Taguchi Design, summarizes how each control factor affects the response at its different levels. It helps identify the optimal factor levels and rank the relative importance of the factors.

Signal to Noise Ratios (S/N) The S/N ratio combines the mean response and variation into a single metric. A higher S/N ratio indicates a more robust setting (better quality with less sensitivity to noise).
Means/Slope
Standard Deviations The table shows shows the average standard deviation of the response at each factor level. It helps identify which factor settings reduce process variation.

The tables include following results

Diagnostics

The diagnostics are displayed in fitted result worksheet, named DOEFittedResult

Standard DOE Diagnotics/Fitted Results

DOE Fitted Results.png

The worksheet presents the fitted results from the standard factorial/RSM analysis

Observation

Observed response values from the experiment.

Fitted Values

Values predicted by the fitted model for each run.

Regular Residuals

The regular residuals also called ordinary or raw residuals, are the differences between the observed response and the fitted response

Standardized Residuals

The Standardized Residuals express the residual relative to an estimate of its standard deviation. This puts residuals on a common scale and makes observations easier to compare.

Studentdized Residuals

The Studentized Residuals are residuals scaled using an estimate of the residual standard deviation that accounts for the observation's leverage.

Studentized Deleted Residual

The Studentized Deleted Residual measures how unusual an observation is after fitting the model without that observation. It is sometimes referred to as an externally studentized residual.

The observation is temporarily removed from the analysis, the model is refitted, and the residual for the omitted observation is then standardized using the resulting model.

Because the observation being evaluated is excluded when estimating the residual variation, the Studentized Deleted Residual can provide a more sensitive indication of potential outliers than the regular residual.

Taguchi Diagnotics/Fitted Results

DOE Taguchi Fitted Results.png

The worksheet shows how well the model predicts three Taguchi quality characteristics simultaneously: S/N ratio (robustness), mean (target performance), and standard deviation (consistency).

In addition to the fitted results and residuals in the standard DOE diagnotics, the taguchi design supports more diagnotics

Hi (Leverage)

How far a run's factor settings are from the design center. Higher values = more potential to pull the fit.

Cook's Distance

How much the fitted values change when that run is removed. Values > 1 suggest a strongly influential point

DFITS

Combines leverage and residual size to measure overall influence on the fit. A large absolute DFITS value means the run pulls the fitted surface toward itself;

Response Summary

The response summary worksheet, named DOERespondSummary, is the raw output used to compute the factor effect summaries that drive Taguchi optimization.

Static Taguchi Design

DOE Taguchi Respond Summary.png

Dynamic Taguchi Design

DOE Taguchi Response Summary Dynamic.png