A Presentation to explain the results.pptx

modeling using minitab

1. A Presentation to explain the results

2. Plackett-Burman designs In 1946, R.L. Plackett and J.P. Burman published their now famous paper "The Design of Optimal Multifactorial Experiments" in  Biometrika  (vol. 33). This paper described the construction of very economical designs with the run number a multiple of four (rather than a power of 2). Plackett-Burman designs are very efficient screening designs when only main effects are of interest. These designs have run numbers that are a multiple of 4 Plackett-Burman (PB) designs are used for screening experiments because, in a PB design, main effects are, in general, heavily confounded with two-factor interactions. 

3. Plackett - Burman Design   Factors: 30 Replicates: 1 Base runs: 32 Total runs: 32 Base blocks: 1 Total blocks: 1

4. Standardized Residual  is the regular residual divided by the constant standard deviation.

5. The  Effect Probability  plot is a linear representation of probability versus the standardized effect (i.e., the probability that any term’s standardized effect will be lower than the given value). The points on this plot represent the values for each term in the T Value column of the Regression Table in the detailed  analysis results . If there is no error in the design, then the probability versus the effect is shown and the points on this plot represent the values for each term in the Effect column of the Regression Table in the analysis results.

6. Residuals Plots Residuals are the differences between the observed response values and the response values predicted by the model at each combination of factorial values. Residuals plots, which are available only when there is error in the design, help to determine the validity of the model for the currently selected response. All residuals plots allow the user to select the type of residual to be used: Regular Residual  is the difference between the observed Y and the predicted Y.

7. The  Main Effects  plot shows the mean effect of the selected factor(s). The points are the observed Y values at the low and high level for each factor. The line connects the mean value at each factor level. Note that if you are using actual factor values in the plot, you can plot only one factor at a time. If you are using coded values, you can plot multiple factors simultaneously.

8. The  Residual vs. Order*  plot shows the residuals plotted against the order of runs used in the design. If the points are randomly distributed in the plot, it means that the test sequence of the experiment has no effect. If a pattern or trend is apparent, this indicates that a time-related variable may be affecting the experiment and should be addressed by randomization and/or blocking. Points outside the critical value lines, which are calculated based on the specified alpha (risk) value, may be outliers and should be examined to determine the cause of their variation.

9. The  Residual vs. Fitted*  plot shows the residuals plotted against the fitted, or predicted, values of the selected response. If the points are randomly distributed around the "0" line in the plot, the model fits the data well. If a pattern or trend is apparent, it can mean either that the model does not provide a good fit or that Y is not normally distributed, in which case a  transformation  should be used for further analysis. Points outside the critical value lines, which are calculated based on the specified alpha (risk) value, may be outliers and should be examined to determine the cause of their variation.

10. The  Residual Histogram*  is used to demonstrate whether the residual is normally distributed by dividing the residuals into equally spaced groups and plotting the frequency of the groups.

11. The  Fitted vs. Actual  plot shows the fitted, or predicted, values of the currently selected response plotted against the actual, or observed, values of the response. If the model fits the data well, the points will cluster around the line.