When you select or augment/improve a D-optimal design, you can specify how to generate the initial design and how to search for improvements to the initial design. Usually, you change the methods to affect how quickly Minitab finds an optimal design. However, other considerations also affect how long Minitab needs to find a solution. For example, the more terms are in the model, the longer the process to find an optimal design.
- Initial Design
- Generated by sequential optimization
- Specify that Minitab selects all points sequentially.
- Usually, generating all of the design points by sequential optimization is more likely to produce an optimal design that has relatively high D-optimality. An initial design with relatively high D-optimality usually leads to a shorter number of search steps to improve the initial design.
- Percentage of design points to be selected
- Specify that Minitab selects some of the design points at random. The more design points Minitab chooses at random, the faster Minitab produces an initial design. However, more random design points also increases the probability that the points form a rank deficient matrix. Rank deficient matrices are more likely as the number of design points to select approaches the minimum number of points that are necessary to fit the terms.
- Number of random trials: Specify how many initial designs to produce. The higher the number, the more likely that the optimal design has relatively high D-optimality. The lower the number, the faster Minitab produces an initial design.
- Base for random data generator: Specify a base for the random data generator so that you can obtain the same optimal design if you select an optimal design from the same set of candidate points again. When you enter the same base, Minitab selects the same random points, if the order of the worksheet remains the same.
- Search Procedure for Improving Initial
- Exchange method with number of exchange
- Usually, the exchange method finds a solution faster than Fedorov's method because the exchange method considers fewer possible designs
- The higher the number of exchange points, the faster the method produces a solution. Minitab adds the best points from the candidate set, then drops the worst points until the D-optimality of the design cannot be improved further.
- Fedorov’s method
- Because Fedorov's method considers more possible designs than the exchange method, Fedorov's method is more likely to find a more D-optimal design.
- Minitab adds one point from the candidate set and drops another point so that the switch results in the maximum improvement in D-optimality. This process continues until the design cannot be improved further.
- Use the initial design. This method is least likely to find the most D-optimal design, but the fastest to complete.