Closed-Form Formulae of Wordlength Pattern for Saturated Resolution IV and III Designs and Their Relationships

解析度IV和III飽和設計的字長樣式之封閉公式及其關係

10.6220/joq.202302_30(1).0002

Jen-der Day(戴貞德)；Hsin-Lu Liu(劉信陸)；Yu-Lin Han(韓育霖)；Tsai-Hsin Cheng(鄭再興)；Hsien-Tang Tsai(蔡憲唐)

complementary theory ； geometrical design ； minimum aberration ； resolution ； two-level fractional factorial design ； 互補理論 ； 幾何設計 ； 最小像差 ； 解析度 ； 兩水準部分實驗設計

品質學報

30卷1期（2023 / 02 / 28）

13 - 25

英文;繁體中文

Based on the wordlength pattern (WLP), resolution and minimum aberration are the two most useful criteria for choosing a good two-level fractional factorial experiment. Using geometrical designs and complementary theory, this paper develops the closed-form formulae of WLP for saturated resolution IV (R-IV) and R-III designs with any run size to overcome the tedious calculation of large-scale design and provide some theoretical background. We also use inductive proof to explore the relationships between and within two saturated designs. These results can be used to develop closed-form formulae of WLP for other special designs.

基於字長樣式，解析度和最小像差是兩個最有用的標準，用以選擇良好的兩水準部分實驗設計。本文利用幾何設計和互補理論，為任意大小規模解析度IV和III飽和設計開發了字長樣式的封閉公式，從而克服了大規模設計的繁瑣計算，並提供了一些理論背景；另外我們還使用歸納證明來探索兩個飽和設計之間的關係。這些結果可用於為其他特殊設計開發字長樣式的封閉公式。

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1. Yu-Lin Han,Tsai-Hsin Cheng,Jen-der Day,Hsin-Lu Liu,Hsien-Tang Tsai(2023)。Binary Column Assignment Method for Two-Level Minimum Aberration Fractional Factorial Designs。品質學報，30(2)，67-88。