Fig. 2 illustrates a ‘‘greedy’’ selection process that would always be made if the SID was not constructed to adhere to position balance. For example, suppose there are n ¼ 396 pan-elists and we wish to construct a 12P6 design. To ensure position balance, we require that each product appears r ¼ 33 times (where r ¼ n=p) in each position, while not letting any panelist rate any one product more than once. Note that, in practice, it will not always be the case that an SID is perfectly balanced. Misuse of the rating apparatus, a non-divisible sample size or neglect on behalf of the panelists are a few of the possible scenarios that could lead to some products being evaluated more than others.