We often face some difficulties when we try to evaluate many objects at once. In that case, paired comparisons are known to be very efficient .Nakaya's version is one of the methods of paired comparisons, in which every member of a panel compares all pairs of objects. Little attention has been paid to the fact that Nakaya's model includes information about variation in the individuals' evaluations. In this paper, we propose a new method to analyse these differences, where PCA is applied to decompose the interaction effects between the panel and the objects in Nakaya's model, emphasizing the importance of examining the individual differences in a panel. Moreover, we point out that the data matrix decomposed in Nishisato's Dual Scaling for paired comparisons data is substantially equivalent to the matrix of the sum of the main effect and the interaction in Nakaya's version. Finally, we show that our method complements both of the above-mentioned methods by connecting them.

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In this paper, we discuss a method of determination of dimensional tolerance based on given data when quality characteristic has dimensional tolerance. First, a method of determination of dimensional tolerance, assuring a probability that quality characteristic satisfies its tolerance, is proposed by an application of 100 β% content tolerance interval with confidence level 1-α. Second, through an application of the method to actual data, it is shown that there are two cases where it is impossible to derive the dimensional tolerance, and a width of the dimensional tolerance is less than a given width. Finally, we evaluate a performance of the method. We also discuss how to determine a sample size of additional experiments to derive the dimensional tolerance (to derive a larger width than given width) based on the result of performance evaluation.

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