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

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.

關鍵字

complementary theory ； geometrical design ； minimum aberration ； resolution ； two-level fractional factorial design

並列摘要

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。

並列關鍵字

互補理論；幾何設計；最小像差；解析度；兩水準部分實驗設計

參考文獻

Day, J.-D., 2017, A heuristic method for planning two-level fractional factorial experiments using basic quaternary design table, Journal of Quality, 24(4), 300-310. doi:10.6220/joq.2017.24(4).05

Block, R. M. and Mee, R. W., 2005, Resolution IV designs with 128 runs, Journal of Quality Technology, 37(4), 282-293. doi:10.1080/00224065.2005.11980331

Box, G. E. P. and Hunter, J. S., 1961, The 2k – p fractional factorial designs: part I, Technometrics, 3(3), 311-351. doi:10.1080/00401706.1961.10489951

Butler, N. A., 2003, Some theory for constructing minimum aberration fractional factorial designs, Biometrika, 90(1), 233-238. doi:10.1093/biomet/90.1.233

Chen, H. and Hedayat, A. S., 1996, 2n – l designs with weak minimum aberration, The Annals of Statistics, 24(6), 2536-2548. doi:10.1214/aos/1032181167

被引用紀錄

Jen-der Day、Hsin-Lu Liu、Tsai-Hsin Cheng、Yu-Lin Han、Hsien-Tang Tsai（2023）。Binary Column Assignment Method for Two-Level Minimum Aberration Fractional Factorial Designs。品質學報，30(2)，67-88。https://doi.org/10.6220/joq.202304_30(2).0001

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