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Abstract
Industrial quality characteristics are often measured categorically rather than numerically, such as by recording a response as “slight,” “moderate,” or “extreme.” Accumulation analysis, a method proposed by Taguchi (1974) for analyzing ordered categorical data from industrial experiments, is used in Japanese industry and is becoming popular in the United States. Nair (1986) proposed using the first two components of the accumulation analysis statistic separately, as well as using simpler alternatives, to detect location and dispersion effects, respectively. We expose some problems with accumulation analysis in the multifactor setting, which is the usual industrial setting, since it is more efficient to investigate many factors simultaneously. Our results show that accumulation analysis detects spurious factor effects and reverses the order of factor importance. Furthermore, reanalysis of data from two real experiments reveals that these problems with accumulation analysis are realized in practice. We demonstrate an inherent problem with detecting dispersion effects from ordered categorical data. Even in the absence of this problem, we show that the dispersion tests still detect spurious effects and reverse the order of factor importance more seriously than does accumulation analysis. On the other hand, the location tests are generally useful, especially Nair's simple alternative, which happens to be the Kruskal–Wallis test. Moreover, we provide an explanation of why location tests provide a particularly sensible method of analysis in the industrial context. We also consider other alternatives—the method of scoring categories, a mean response model, and a proportional odds model. The method of scoring the categories is simple and particularly effective if the scores are reasonably chosen.
