Find definitions and interpretation guidance for every design optimality statistic.

The condition number measures the collinearity among model terms. When you compare designs, a smaller condition number is better.

Use the condition number to compare different optimal designs or to compare the same design with different terms. A condition number of 1 indicates that the model terms are orthogonal. Larger values indicate more collinearity.

Most optimal designs are not orthogonal. Because terms in the model are not independent, the interpretation of non-orthogonal designs is less straightforward than the interpretation of orthogonal designs.

In these results, the condition number indicates that the data exhibit moderate to strong collinearity.

Row number of selected design points: 46, 54, 36, 8, 44, 47, 31, 55, 30, 43, 38, 59, 62, 15,

56, 24, 42, 20, 32, 16, 6, 45, 19, 17, 25, 49, 64, 10, 37, 1, 39, 3

56, 24, 42, 20, 32, 16, 6, 45, 19, 17, 25, 49, 64, 10, 37, 1, 39, 3

Condition number: | 259.114 |
---|---|

D-optimality (determinant of XTX): | 7.92282E+28 |

A-optimality (trace of inv(XTX)): | 12.1719 |

G-optimality (avg leverage/max leverage): | 0.96875 |

V-optimality (average leverage): | 0.96875 |

Maximum leverage: | 1 |

D-optimality indicates the design's ability to obtain precise estimates or predictions. When you compare designs, a larger D-optimality value is better.

You can use optimality metrics to compare designs, but remember that the optimality of a given D-optimal design is model dependent. That is, optimality is defined for a fixed design size and for a particular model.

In these results, the first optimal design has 25 design points and the second optimal design has 20 design points. The first design has a higher D-optimality statistic than the second optimal design, which is expected with more runs.

- Optimal design with 25 design points
- Response surface design augmented according to D-optimalityNumber of candidate design points: 30Number of design points to augment/improve: 20Number of design points in optimal design: 25Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design augmented by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

Row number of selected design points: 1, 3, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 22, 23, 24,

25, 26, 27, 28, 30, 2, 5, 14, 18, 20Condition number: 8.53018 D-optimality (determinant of XTX): 3.73547E+20 A-optimality (trace of inv(XTX)): 1.99479 G-optimality (avg leverage/max leverage): 0.64 V-optimality (average leverage): 0.64 Maximum leverage: 1 - Optimal design with 20 design points
- Response surface design selected according to D-optimalityNumber of candidate design points: 30Number of design points in optimal design: 20Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design generated by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

Row number of selected design points: 22, 23, 25, 27, 4, 8, 19, 2, 14, 15, 13, 6, 9, 3, 16,

24, 28, 30, 26, 1Condition number: 10.2292 D-optimality (determinant of XTX): 2.73819E+18 A-optimality (trace of inv(XTX)): 2.50391 G-optimality (avg leverage/max leverage): 0.8 V-optimality (average leverage): 0.8 Maximum leverage: 1

A-optimality measures the average variance in the regression coefficients of the fitted model. When you compare designs, a smaller A-optimality value is better.

You can use optimality metrics to compare designs, but remember that the optimality of a given A-optimal design is model dependent. That is, optimality is defined for a fixed design size and for a particular model. Designs that are more D-optimal are not necessarily more A-optimal.

In these results, the first optimal design has 25 design points and the second optimal design has 20 design points. The first design has a lower A-optimality statistic than the second optimal design, which is expected with more runs.

- Optimal design with 25 design points
- Response surface design augmented according to D-optimalityNumber of candidate design points: 30Number of design points to augment/improve: 20Number of design points in optimal design: 25Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design augmented by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

Row number of selected design points: 1, 3, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 22, 23, 24,

25, 26, 27, 28, 30, 2, 5, 14, 18, 20Condition number: 8.53018 D-optimality (determinant of XTX): 3.73547E+20 A-optimality (trace of inv(XTX)): 1.99479 G-optimality (avg leverage/max leverage): 0.64 V-optimality (average leverage): 0.64 Maximum leverage: 1 - Optimal design with 20 design points
- Response surface design selected according to D-optimalityNumber of candidate design points: 30Number of design points in optimal design: 20Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design generated by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

Row number of selected design points: 22, 23, 25, 27, 4, 8, 19, 2, 14, 15, 13, 6, 9, 3, 16,

24, 28, 30, 26, 1Condition number: 10.2292 D-optimality (determinant of XTX): 2.73819E+18 A-optimality (trace of inv(XTX)): 2.50391 G-optimality (avg leverage/max leverage): 0.8 V-optimality (average leverage): 0.8 Maximum leverage: 1

G-optimality is the ratio of the average prediction variance to the maximum prediction variance over the design points. G-optimal designs minimize the denominator, while V-optimal designs minimize the numerator. Ideally, you want both the numerator and denominator to be smaller values.

You can use optimality metrics to compare designs, but remember that the optimality of a given G-optimal design is model dependent. That is, optimality is defined for a fixed design size and for a particular model. Designs that are more D-optimal are not necessarily more G-optimal.

In these results, the first optimal design has 25 design points and the second optimal design has 20 design points. The design with more points is less G-optimal than the design with more points, even though the larger design is more D-optimal.

- Optimal design with 25 design points
- Response surface design augmented according to D-optimalityNumber of candidate design points: 30Number of design points to augment/improve: 20Number of design points in optimal design: 25Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design augmented by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

Row number of selected design points: 1, 3, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 22, 23, 24,

25, 26, 27, 28, 30, 2, 5, 14, 18, 20Condition number: 8.53018 D-optimality (determinant of XTX): 3.73547E+20 A-optimality (trace of inv(XTX)): 1.99479 G-optimality (avg leverage/max leverage): 0.64 V-optimality (average leverage): 0.64 Maximum leverage: 1 - Optimal design with 20 design points
- Response surface design selected according to D-optimalityNumber of candidate design points: 30Number of design points in optimal design: 20Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design generated by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

Row number of selected design points: 22, 23, 25, 27, 4, 8, 19, 2, 14, 15, 13, 6, 9, 3, 16,

24, 28, 30, 26, 1Condition number: 10.2292 D-optimality (determinant of XTX): 2.73819E+18 A-optimality (trace of inv(XTX)): 2.50391 G-optimality (avg leverage/max leverage): 0.8 V-optimality (average leverage): 0.8 Maximum leverage: 1

V-optimality measures the average prediction variance over the set of design points. When you compare designs, a smaller V-optimality value is better.

You can use optimality metrics to compare designs, but remember that the optimality of a given V-optimal design is model dependent. That is, optimality is defined for a fixed design size and for a particular model. Designs that are more D-optimal are not necessarily more V-optimal.

In these results, the first optimal design has 25 design points and the second optimal design has 20 design points. The first design has a lower V-optimality statistic than the second optimal design, which is expected with more runs.

- Optimal design with 25 design points
- Response surface design augmented according to D-optimalityNumber of candidate design points: 30Number of design points to augment/improve: 20Number of design points in optimal design: 25Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design augmented by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

25, 26, 27, 28, 30, 2, 5, 14, 18, 20Condition number: 8.53018 D-optimality (determinant of XTX): 3.73547E+20 A-optimality (trace of inv(XTX)): 1.99479 G-optimality (avg leverage/max leverage): 0.64 V-optimality (average leverage): 0.64 Maximum leverage: 1 - Optimal design with 20 design points
- Response surface design selected according to D-optimalityNumber of candidate design points: 30Number of design points in optimal design: 20Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CDInitial design generated by Sequential methodInitial design improved by Exchange methodNumber of design points exchanged is 1
## Optimal Design

24, 28, 30, 26, 1Condition number: 10.2292 D-optimality (determinant of XTX): 2.73819E+18 A-optimality (trace of inv(XTX)): 2.50391 G-optimality (avg leverage/max leverage): 0.8 V-optimality (average leverage): 0.8 Maximum leverage: 1

Maximum leverage indicates that a design has a highly influential point when the maximum leverage is much larger than V-optimality. Minitab uses this value in the denominator when calculating G-optimality.

Use maximum leverage to determine when a design contains at least one influential point. Designs that are more D-optimal can have influential points.

In these results, the maximum leverage is 1 and the V-optimality is 0.8. In this optimal design, none of the factor levels in row 2 are in any of the other points.

Response surface design selected according to D-optimality

Number of candidate design points: 30

Number of design points in optimal design: 20

Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CD

Initial design generated by Sequential method

Initial design improved by Exchange method

Number of design points exchanged is 1

24, 28, 30, 26, 1

Condition number: | 10.2292 |
---|---|

D-optimality (determinant of XTX): | 2.73819E+18 |

A-optimality (trace of inv(XTX)): | 2.50391 |

G-optimality (avg leverage/max leverage): | 0.8 |

V-optimality (average leverage): | 0.8 |

Maximum leverage: | 1 |

Minitab displays the largest and smallest distances between the selected design points. This value is the Euclidean distance.

The difference between the largest and the smallest distance values indicates how uniformly the points are spread in the design space. You can use this information to compare designs.