On Measures of Coefficients for Classification of Cumulative Curves with the Grey Theory

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  • 灰色理論を用いた流動数曲線における形状とパラメーターの関係
  • ハイイロ リロン オ モチイタ リュウドウスウ キョクセン ニ オケル ケイジョウ ト パラメーター ノ カンケイ

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Abstract

The cumulative curve is an analytic technique that is used for the improvement of production processes and planning in manufacturing. We have already proposed that the cumulative curve can be expressed as GM (1,1) and GM (1,2) models. This paper discusses the problem of classification for cumulative curve and the characteristic of coefficients in GM (1,1) and GM (1,2) models. The coefficients of the cumulative curve for the nine shapes are computed from the Grey Theory. The variations of curve are given as the differences of slope and curvature of the cumulative curve. This paper shows that all kinds of cumulative curves are classified into five basic curves. The classification of cumulative curves can be computed from the coefficients of the GW (1,1) and GM(1,2) models. The classification of curves is used with the Mahalanobis distance in discriminant analysis. The proposed method has also been tested by using numerical examples. This paper shows that all kinds of cumulative curves can be given as the coefficients of GM (1,1) and GM (1,2) models.

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