# Modified Extensible Lattice Sequence (Mels)

A lattice sequence is a quasi-random sequence, or low discrepancy sequence, designed to equally spread out points in a space by minimizing clumps and empty spaces.

This property makes lattice sequences an excellent space filling DOE scheme. This DOE type also has the property of extensibility, which means the method can take an existing set of data in a space, and add more data points to provide equal coverage; although with Modified Extensible Lattice Sequence it is optimal to extend on to Modified Extensible Lattice Sequence data. The number of runs is specified by the user.

## Usability Characteristics

• Use for exploring the entire design space and creating fitting functions to the exact output responses. It is the recommended default space filling scheme.
• To get a good quality fitting function, a minimum number of runs should be evaluated. (N+1)(N+2)/2 runs are needed to fit a second order polynomial, assuming that most output responses are close to a second order polynomial within the commonly used input variable ranges of -+10%. An additional number of runs equal to 10% is recommended to provide redundancy, which results in more reliable post-processing. As a result, this equation is recommend to calculate the number of runs needed or a minimum of 1.1*(N+1)(N+2)/2 runs.
• Add existing data to the inclusion matrix to use the extensibility feature. While any data can be used as an inclusion, the best performance can be expected when the inclusion is an existing data set from a Modified Extensible Lattice Sequence DOE.
• Supports input variable constraints.
• When building a Modified Extensible Lattice Sequence DOE with the intention of using it as a Testing matrix, the resulting Testing matrix could be a subset of the Modified Extensible Lattice Sequence based input matrix due to the extensible property of Modified Extensible Lattice Sequence. To prevent this from happening, change the Random Seed setting of the Testing matrix to be a number larger than the number of runs in the Input data before building it.

## Settings

In the Specifications step, Settings tab, change method settings.
Parameter Default Range Description
Number of Runs $\frac{1.1\left(N+1\right)\left(N+2\right)}{2}$ > 0 integer Number of new designs to be evaluated.
Sequence Offset 1 Integer

0 to ∞

Controls the starting offset for the Modified Extensible Lattice Sequence sequence. For example, a value of 101 starts the generated evaluation points from the 101st point of the Modified Extensible Lattice Sequence.
Note: In the presence of input variable constraints, the algorithm may skip runs, resulting in interal sequence of Modified Extensible Lattice Sequence to be different than the Sequence Offset defined by the user. Take note of duplicate runs prior to evaluation. If possible, the inclusion matrix method is recommended.