During the design phase of DfSS, developers derive a transfer function that translates design parameters into quality characteristics (CTQs). However, since there are usually several important CTQs, and these can be correlated, from a statistical point of view creating separate transfer functions for the various CTQs is not always your best solution. Which brings us into the realm of multivariate statistics.

**Perception-related CTQs**

There is an additional complicating factor if CTQs are consumer perception-related (e.g. “consumer rating on aspect x should be at least 7/10” or “probability of purchasing product should be at least 80% for target group y”). First, because we can’t measure perception directly, only obtain perception data by asking the subject. And secondly, because it may be difficult/inappropriate to measure the same aspect twice on one consumer, since the measuring process itself can change that person’s perception.

In addition, many different possible consumer-related aspects can be observed, which makes it important to have a hypothetical causal model about the psyche of the consumer. Generally speaking, unobservable/unobserved (or ‘latent’) factors — such as attitude, intelligence, motivation, etc — are vital in such a model.

**The attraction of SEMs**

Combining the need for one model for multiple CTQs with the need for the model to include latent constructs has resulted in the statistical technique of Structural Equation Models (SEMs). An attractive feature of SEM is that the model can be visualized in a standard way, using blocks for measured factors, circles for unobserved factors and arrows for causal relations. For example:

This diagram indicates that we want to model purchase intent, and hypothesize that the purchase intent is influenced by both Design Factor D1 (which we can measure and control) and the consumer’s motivation.

While it’s impossible to measure a consumer’s motivation directly, we can measure derived quantities using questionnaires. Resulting in scores X1, X2 and X3. Using SEM, we can then estimate the size and uncertainty of the effect of D1 on purchase intent, and perform formal hypothesis tests. Likewise, we can estimate the size and uncertainty of the effect of motivation on purchase intent. It’s worth noting that this would not have been possible using a standard multivariate regression model (regressing purchase intent on X1, X2, X3 and D1), since it would ignore the fact that X1, X2 and X3 are measurements of the same construct, and therefore expected to be correlated.

The above is just one simple example of SEM. Its application can be extended in various ways to provide extremely useful insights in certain specific situations.

For more information on SEM and its applications, contact erwin.stinstra@cqm.nl at CQM.