Space-filling is a type of design of experiments that aims to create a set of experimental runs that are evenly spaced throughout the experimental space, in order to capture the full range of variation in the factors being studied.
They can be very useful as an initial starting experiment to better understand your design space and factors, helping identify appropriate levels to take forwards for an optimization experiment using an Optimal design. They are less useful for optimizing when you have a known good starting point for your factors and their levels, as they are less efficient and have limited statistical power to detect high-order effects, such as 2nd or 3rd order interactions.
Factors can be sampled continuously within the range of the specific factor levels you have defined - or can be sampled discretely. Space-filling designs that sample across a range will give better coverage and insight into the shape of the design space - but will result in a large number of runs (Figure 1). When sampling across a range, any one run in your space-filling design will be completely unique from another, no factor levels will be shared across any other runs. While this can give you a very fine grained screen of your experimental space it has the downside of being a less powerful design as you have no replication of any factor levels across any of your runs.
Sampling discretely will save you runs but with no prior knowledge, you could draw a misleading conclusion about your space, however with some prior knowledge you can set levels appropriately to save runs and still capture the shape of the space (Figure 1).
Figure 1. Sampling numerical factors continuously or discretely in space-filling DOE designs.
Space-filling designs are best suited to exploring a new system, particularly when you have limited prior knowledge about the system. The distribution of sampling points enables you to capture a broad snapshot of performance across your design space. The distribution of runs across a particular factor axis allows for mapping of the shape of your response landscape, making them ideally suited to identifying the “hot spots” in a design space.
With this knowledge, you can move forward with confidence, set appropriate upper and lower limits for your factor levels, and iterate through your DOE campaign with confidence that you are unlikely to fall foul of poorly defined factor levels when going into your optimisation stages.
In summary, typically, space-filling designs are applied when i) you don’t have a good understanding of where to place the levels for your factors and ii) you have sufficient resources to run a high number of experiments. They allow rapid mapping of a large experimental space but have limited statistical power for getting deep insight into the complex behaviour of a given system. They can be good designs for fitting a model to screen for the factors having an impact on your system but often can lack the power to fit a high quality model that will allow you to optimise and make predictions from.
To learn about the statistics behind space-filling designs, click here.
To learn how to calculate a space-filling design, click here.
To learn about other design types, click here.