Binary Column Assignment Method for Two-Level Minimum Aberration Fractional Factorial Designs

兩水準最小像差部分設計的二進制行配置法

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

《品質學報》 30卷2期 (2023/04) Pp. 67-88

https://doi.org/10.6220/joq.202304_30(2).0001

摘要

Weighing the pros and cons between the resolution and experimental runs, we believe that resolution III designs still have practical value and are worthy of attention. This paper uses the binary representation of the number of factors and proposes a binary column assignment method for constructing minimum aberration (MA) geometrical designs. Then we develop a combinatorial algorithm and the closed-form formulae for the wordlength pattern (WLP) of a right-half resolution III (R-III) design, which can be used to calculate the WLPs for (1) all R-III MA designs from 8 to 256 runs; (2) a family of R-III MA designs constructed by using MA 128-run designs; and (3) the large R-III weak MA designs.

關鍵字

geometrical design ； minimum aberration ； resolution ； right-half R-III design ； wordlength pattern

並列摘要

權衡解析度和實驗次數之間的利弊，可以得知解析度III的設計仍然有其實用價值且值得關注。本文運用因子數的二進制表示法，提出了二進制行配置法來建構具有最小像差的兩水準部分幾何設計。之後，我們為右半解析度III部分設計的字長樣式開發了組合演算法和封閉公式，其可用於計算下列三種特殊設計的字長樣式：（1）具有8到256實驗次數的所有解析度III且最小像差的部分設計；（2）運用128實驗次數最小像差設計所建構的解析度III且最小像差的部分設計之系列；（3）大型解析度III且弱最小像差的部分設計。

並列關鍵字

幾何設計 ； 最小像差 ； 解析度 ； 右半解析度III設計 ； 字長樣式

參考文獻

Day, J.-d., Liu, H.-L., Han, Y.-L., Cheng, T.-H. and Tsai, H.-T., 2023, Closed-form formulae of wordlength pattern for saturated resolution IV and III designs and their relationships, Journal of Quality, 30(1), 13-25. doi:10.6220/joq.202302_30(1).0002

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