Visit filling plans (or space-filling designs are a class of experimental designs widely used in process optimization, particularly in situations where the experimental design is not well defined beforehand. They are designed to explore a space of factors in a uniform way, without any preconceived ideas about the shape of the relationship between factors and response. They are particularly useful in numerical simulation studies, computer experiments and complex response surface models.
Ellistat Data Analysis offers several types of filling plans:
- Latin hypercube Latin Hypercube Sampling is based on dividing each dimension of factor space into equal intervals. Unlike simple random sampling, LHS ensures that there is exactly one point in each interval of each dimension. This guarantees uniform coverage of the experimental space, minimizing sampling bias and improving statistical efficiency.
- Audze-Eglais Hypercube The Latin Hypercube: is a specific approach to the filling plane that combines the characteristics of the Latin Hypercube with a uniformity measure developed by Audze and Eglais. This technique is used to generate samples in parameter space in such a way as to optimize the distribution and uniformity of points, thus minimizing sampling bias. This results in a more homogeneous coverage of the space, which is essential for complex optimization and modeling studies, especially when using expensive simulation models.
- NOLH: The Nearly Orthogonal Latin Hypercubes (NOLH) experimental designs are an improved version of Latin Hypercubes (LHS), which allow systematic exploration of factor space while minimizing correlation between variables. They are particularly effective for experiments requiring the consideration of many variables while preserving a low number of trials. The NOLH was developed to overcome the correlation limitations of conventional Latin hypercubes, by providing an almost orthogonal design, meaning that the correlation between columns is close to zero.
Example: Filling plan
In the company ElliPrecision is an automotive components manufacturer specializing in the production of engine pistons. To improve the quality of these pistons, the company wanted to optimize three critical parameters of the manufacturing process: forging temperature (between 850°C and 950°C), casting pressure (from 100 MPa to 150 MPa), cooling time (from 15 to 30 minutes) and holding time (from 45 min to 60 min). Using a Latin Hypercube filling pattern, ElliPrecision seeks to assess the impact of these factors on piston performance, in order to guarantee longer-lasting, more efficient products.
Factors considered
- Forging temperature (between 850°C and 950°C)
- Casting pressure (from 100 MPa to 150 MPa)
- Cooling time (15 to 30 minutes)
- Holding time (from 45 min to 60 min)
Measured Response
- stress at break Rm (MPa)): Measured in megapascals (MPa).
Filling plan (Latin Hypercube plan)
A Latin Hypercube (LHC) design is a sampling method that divides each factor into several levels so that each level is represented uniformly. This allows the parameter space to be covered more efficiently than a simple full factorial design, especially when the number of trials has to be limited.
Generating the test matrix with Ellistat
- Click on the "DOE"Then click on the "filling plan**"**.
- In the zone 1You can set the tab name and choose the experimental design array. 📝: Set tab name "ElliPrecision"Then select the "composite" design.
- In zone 2, we can put the number of factors, name them then put the value of the min and max 📝: Put 4 factors :
- Forging temperature (between 850°C and 950°C)
- Casting pressure (from 100 MPa to 150 MPa)
- Cooling time (15 to 30 minutes)
- Holding time (from 45 min to 60 min)
- In zone 3, you'll find a preview of the test matrix, which will be generated in the tab created in zone 1. You can also create a D-optimal design, which is a type of experimental design that aims to maximize the statistical efficiency of an experiment while minimizing the number of trials required. 📝: Click on "Create DOE".
- In ElliWelding" gridThis is the test matrix. This matrix contains the minimum and maximum level values entered during plan creation, as well as other intermediate values which generate tests evenly distributed in the factor space.
- In the next column you can manually add the trial run results as shown in the following figure: DOE filling
