Using supersaturated designs to plan effective experiments

Supersaturated designs are becoming popular in industrial experimentation because they are highly cost-efficient. In the initial stages of an industrial experiment, the set of factors which may influence the response is chosen to be large. However, the actual number of factors affecting the response is generally small (known as the effect sparsity problem).

Japanese engineer and statistician Genichi Taguchi identified that there are two types of inputs in a production process: the easy-to-manipulate ones, which are known as the control factors, and the difficult-to-manipulate ones, or noise factors.

The noise factors are the sources of variations in a process response when a system is used in practice, but they can be controlled in an experimental environment.

A supersaturated design such as the one shown in Figure 1 could help, for example, a tractor company study the importance of the presence of 14 safety factors (columns) by manufacturing only 8 tractors (rows). Here 1 and -1 represent the presence and absence respectively of a safety factor in the tractor.

The main objective of robust parameter designs is to determine the settings of the control factors that achieve a desired mean response as well as make the process robust, or insensitive, to the effects of noise variables.

However, when the number of factors affecting the response is large, the huge number of experimental runs needed to fit all the factors and their interactions adds to the cost of the experiment.

This is where the application of supersaturated experiments in robust parameter designs proves to be economically beneficial. And this is where Rakhi Singh, a researcher with the IITB-Monash Research Academy, is hoping to make a difference.

Rakhi is working on a project titled, ‘Fractional Factorial and Related Designs — Optimality and Construction’, and she hopes to design cost- and time-effective experiments for the benefit of industry and government. More precisely, she has ventured into the area of ‘Choice experiments’ and ‘Supersaturated designs’.

“Choice experiments mirror real-world situations closely and help manufacturers, service-providers, policy-makers, and other researchers to take business decisions on the characteristics of their products and services based on the perceived utility to customers,” explains Rakhi. Typically, industry employs supersaturated designs to ascertain the few factors that are active and most critical (among a large number of factors present) in influencing the characteristics of a product or service.

Figure 2. An example of a choice question asked in a marketing survey by car companies

“By definition, this work is challenging since it involves doing theoretical mathematics. What enthuses me the most is that I have the freedom to experiment (through computer simulations) and judge which ideas may or may not work. Once an idea is judged to be worthy, rigorous mathematics is involved to prove that the idea actually works in the conceptual phase. Another reason I find my research exciting is that it will help industries take informed decisions on vital questions they face on a day-to-day basis.”

The IITB-Monash Research Academy is a collaboration between India and Australia that endeavours to strengthen scientific relationships between the two countries. Graduate research scholars like Rakhi study for a dually-badged PhD from both IIT Bombay and Monash University, spending time at both institutions to enrich their research experience.

Says Prof Murali Sastry, CEO of the Academy, “We hope that research scholars like Rakhi will be able to offer mathematics-based solutions to bridge the gap between industry and academics, particularly in developing countries like India, by designing cost- and time-effective experiments that will benefit both industry and government.”