Minitab procedures for Exam - Toolbox - prof. Portioli

AHPMatrices

Matrix structure

1 matrix: criteria vs criteria with respect to the goal.

• "x" matrices: subcriteria vs subcriteria with respect to their "parent" criteria (for each criteria that has subcriteria).
• "n" matrices: alternatives vs alternatives with respect to all the lower level criteria.

Check consistency: CR > 0.1

Final decision calculation

1. Calculate the rating of the criteria and subcriteria, as well as the rating of the alternatives with respect to the criteria and subcriteria.
2. Calculate the final rating (overall priority) of each alternative by multiplying and summing rating of criteria and rating of alternative against each criterion/subcriterion.
3. Rank alternatives using overall priority (highest value is the 100%, all the others are: value/value max).

• Overall Priority (alt 1) = alt1*AVE(subcrit1)*WEIGHT(subcrit1) + alt1*AVE(subcrit2)*WEIGHT(subcrit2) + alt1*AVE(criteria2) + alt1*AVE(criteria3) + …
• Overall Priority (alt 2) = alt2* …
• Overall Priority (alt 3) = alt3* …

⟹ Project with highest value is the best one

+ We could do a sensitivity analysis (What if analysis) → if all criteria equal (only main criteria)

Anova One Way

Analysis steps

Stat → Anova → One way

• Response = outcome of the experiment (Y)
• Factor = process variables that affect the output (in 1 way: 1 factor)

Storage: Residuals

Graph: all graphs

Options: Confidence level = 95%

Graphs and metrics

• Boxplot → idea of the distribution of the sample (check outliers) →
• Normal probability plot to understand if the distribution is normal (S line is normal)
• P-value → if < 0.05, we reject the null hypothesis (⟹ exists at least one μ different from the others) and so the factor is significant in terms of impact on the response variable
• Standard deviation (S) → standard deviation of the distance between data values and fitted values (budgeted). It tells how well the model describes the response (the lower the better!)
• F-value → MS (factor) / MS (error) (the higher the better)
• R-sq(adj) (= 1 – (MSerr/MStot)) → percentage of variation in the response that is explained by the model. The factors that are included in the model are explaining the "R-sq(adj)"% of the variation that is present in the response variable (a good value is higher than 70%). → If p-value < 0.05 and R-sq(adj) is very low, it means that we did not take into account other factors that are having an impact on the y variable.
• R-sq = 1 – (SS error / SS total)

Usually it is better to consider the Rsq(adj) since it is more conservative as it is taking into consideration the number of predictors and the number of observations that are in the model.

• R-sq(pred) tells which is the fit of the model, so which is the capability of the model to predict new variables. →
• Mean the best one is the one that has the highest value because we want to maximize the response variable.