基于非均衡序贯设计的大规模关键质量因子筛选研究

doi:10.16381/j.cnki.issn1003-207x.2024.1184

摘要/Abstract

摘要：

随着系统复杂度的提高，涉及到的因子数目越来越大，采用尽可能低的试验成本识别出显著影响质量特性的关键因子是质量改进活动中的重要环节。针对大规模关键质量因子筛选中样本有限性、试验经济性以及数据的非均衡特征等问题，本文提出了基于非均衡序贯设计的大规模因子筛选方法。首先，构建同时考虑因子的位置及散度效应的一阶模型，并且结合序贯分支方法的基本假设及框架，提出了综合应对两种非均衡数据的大规模因子筛选方法SB-UB；然后，针对两种非均衡数据类型，分别提出改进的Bradley-Blackwood方法以及融合F检验以及学生t检验的双重检验法，同时检验因子（组）的位置及散度效应；最后，采用蒙特卡洛仿真试验说明所提的大规模因子筛选方法SB-UB的有效性及稳健性。

关键词: 非均衡设计, 大规模因子, 因子筛选, 序贯分支方法, 散度效应

Abstract:

As system complexity increases， identifying key factors that significantly affect quality characteristics with minimal experimental cost becomes a critical step in quality improvement activities. However， challenges such as limited samples， economic constraints of experimentation， and the presence of unbalanced data necessitate the development of new factor screening methods. A large-scale factor screening approach based on unbalanced sequential design is introduced to address these issues.First， a first-order model that simultaneously considers both location and dispersion effects of factors is constructed. Integrating the fundamental assumptions and framework of sequential bifurcation （SB）， the SB-UB method is proposed to handle two types of unbalanced data. For the first type of unbalanced data， an improved Bradley-Blackwood test is introduced， while for the second type， a dual test combining F-test and Student’s t-test is proposed. Both methods aim to examine the significance of the location and dispersion effects of the factors. Monte Carlo simulation experiments demonstrate the effectiveness and robustness of the proposed SB-UB method for large-scale factor screening. By incorporating both location and dispersion effects， this approach enhances the accuracy of identifying critical quality factors while maintaining a low experimental cost.To validate the method， several simulation experiments， including large-scale simulation systems such as supply chain models， are presented. These systems often involve dozens or even hundreds of factors， far exceeding the capabilities of traditional factor screening methods， which are typically designed for problems involving fewer than 20 factors. The proposed method allows for effective screening even when unbalanced data， due to the use of multiple devices with differing computational capacities， impacts the quality of experimental results. The primary results of this research contribute to the field of quality improvement by providing a robust method to identify key factors under challenging conditions of unbalanced and large-scale data. The integration of advanced statistical testing techniques into the SB framework significantly improves the ability to detect both location and dispersion effects. Furthermore， a gap in the literature is filled by addressing the unbalanced data problem in factor screening， which has been largely overlooked in the field of simulation-based system analysis.In conclusion， the proposed SB-UB method not only advances the sequential bifurcation approach but also provides practical solutions for large-scale factor screening under unbalanced conditions， aiding engineers and researchers in making informed decisions about critical quality factors. The research findings are expected to have broad applications in areas such as supply chain management， service science， and various engineering fields.

Key words: unbalanced design, large-scale factors, factor screening, sequential bifurcation method, dispersion effects

中图分类号:

F273.2

刘丽君, 马义中, 龚本刚, 吴锋, 唐丽娜. 基于非均衡序贯设计的大规模关键质量因子筛选研究[J]. 中国管理科学, 2025, 33(2): 84-94.

Lijun Liu, Yizhong Ma, Bengang Gong, Feng Wu, Lina Tang. Key Quality Factor Screening for Large-Scale Simulation Based on Unbalanced Sequential Design[J]. Chinese Journal of Management Science, 2025, 33(2): 84-94.

图/表 10

图1

表1

SB-UB与经典SB方法及相关衍生方法比较"

文献	随机项	位置	散度	样本量	非均衡
文献[8]	——	√	×	固定	×
文献[9]	$N (0, σ 2)$	√	×	固定	×
文献[10]	$N (0, σ 2 (x))$	√	×	可变	×
文献[15]	$N (0, σ 2 (x))$	√	√	可变	×
文献[16]	$N (0, σ 2 (x))$	√	√	可变	×
本文方法	$N (0, σ 2 (x))$	√	√	固定	√

表1

图2

图3

表2

图4

表3

表4

图5

表5

参考文献 26

1	欧阳林寒，陶宝平，马妍. 基于选择性集成核高斯过程模型的质量预测研究［J］. 中国管理科学， 2023， 31（3）： 69-80.
	Ouyang L H， Tao B P， Ma Y. Research on quality prediction based on gaussian process model with selective ensemble kernel［J］. Chinese Journal of Management Science， 2023， 31（3）： 69-80.
2	施文，渠玉杰，蒋国银. 基于随机Kriging的汽车品牌质量序贯主题比较研究［J］. 中国管理科学， 2023， 31（11）： 114-127.
	Shi W， Qu Y J， Jiang G Y. Comparative study on sequential topics of automobile brand quality based on stochastic kriging［J］. Chinese Journal of Management Science， 2023， 31（11）： 114-127.
3	Wu C F J， Hamada M S. Experiments： Planning， analysis， and optimization［M］. （2nd ed.）.New York：John Wiley & Sons， 2009.
4	Kleijnen J P C. Design and analysis of simulation experiments［M］.（2nd ed.）. Switzerland：Springer， 2015.
5	Shi W， Chen X， Shang J. An efficient Morris method-based framework for simulation factor screening［J］. INFORMS Journal on Computing， 2019， 31（4）： 745-770.
6	Shi W， Chen X. Cluster sampling for Morris method made easy［J］. Naval Research Logistics， 2021， 68（4）： 412-433.
7	Morris M D. Factorial sampling plans for preliminary computational experiments［J］. Technometrics， 1991， 33（2）： 161-174.
8	Bettonvil B， Kleijnen J P C. Searching for important factors in simulation models with many factors： Sequential bifurcation［J］.European Journal of Operational Research， 1997， 96（1）： 180-194.
9	Cheng R C. Searching for important factors： Sequential bifurcation under uncertainty［C］//Proceedings of the 29th conference on Winter simulation，Atlanta Georgia USA， December 7-10 ， IEEE Computer Society，1997： 275-280.
10	Wan H， Ankenman B E， Nelson B L. Controlled sequential bifurcation： A new factor-screening method for discrete-event simulation［J］.Operations Research， 2006， 54（4）： 743-755.
11	Wan H， Ankenman B E， Nelson B L. Improving the efficiency and efficacy of controlled sequential bifurcation for simulation factor screening［J］. INFORMS Journal on Computing， 2010， 22（3）： 482-492.
12	Brenneman W A， Nair V N. Methods for identifying dispersion effects in unreplicated factorial experiments［J］. Technometrics， 2001， 43（4）： 388-405.
13	Arvidsson M， Kammerlind P， Hynén A， et al. Identification of factors influencing dispersion in split-plot experiments［J］. Journal of Applied Statistics， 2001， 28（3-4）： 269-283.
14	Kim K J， Lin D K J. Optimization of multiple responses considering both location and dispersion effects［J］. European Journal of Operational Research， 2006， 169（1）： 133-145.
15	Ankenman B E， Cheng R C H， Lewis S M. Screening for dispersion effects by sequential bifurcation［J］. ACM Transactions on Modeling and Computer Simulation， 2015， 25（1）： 1-27.
16	刘丽君，马义中，欧阳林寒，等. 基于位置和散度效应因子分类筛选及仿真试验［J］. 系统工程理论与实践， 2017， 37（11）： 2854-2862.
	Liu L J， Ma Y Z， Ouyang L H， et al. Screening for location and dispersion effects simultaneously by sequential bifurcation［J］. Systems Engineering - Theory & Practice， 2017， 37（11）： 2854-2862.
17	刘丽君，马义中，欧阳林寒. 高效的因子分类筛选方法及仿真应用［J］. 系统管理学报， 2021， 30（1）： 3-13.
	Liu L J， Ma Y Z， Ouyang L H. An efficient factor screening and classification procedure based on multi-response sequential bifurcation and applications ［J］. Journal of Systems & Management， 2021， 30（1）： 3-13.
18	Liang X W， Jiang A P， Li T， et al. LR-SMOTE—An improved unbalanced data set oversampling based on K-means and SVM［J］. Knowledge-Based Systems， 2020， 196： 105845.
19	Tanha J， Abdi Y， Samadi N， et al. Boosting methods for multi-class imbalanced data classification： An experimental review［J］. Journal of Big data， 2020（7）： 1-47.
20	Zhang T， Chen J， Li F， et al. Intelligent fault diagnosis of machines with small & imbalanced data： A state-of-the-art review and possible extensions［J］. ISA transactions， 2022， 119： 152-171.
21	Shi Q， Zhang H. Fault diagnosis of an autonomous vehicle with an improved SVM algorithm subject to unbalanced datasets［J］. IEEE Transactions on Industrial Electronics， 2020， 68（7）： 6248-6256.
22	Shaw R G， Mitchell-Olds T. ANOVA for unbalanced data： An overview［J］. Ecology， 1993， 74（6）： 1638-1645.
23	Akritas M G， Arnold S F， Brunner E. Nonparametric hypotheses and rank statistics for unbalanced factorial designs［J］. Journal of the American Statistical Association， 1997， 92（437）： 258-265.
24	Skillings J H， Mack G A. On the use of a Friedman-type statistic in balanced and unbalanced block designs［J］. Technometrics， 1981， 23（2）： 171-177.
25	Bettonvil B. Detection of important factors by sequential bifurcation［M］. Tilburg：Tilburg University Press， 1990.
26	Bradley E L， Blackwood L G. Comparing paired data： A simultaneous test for means and variances［J］. The American Statistician， 1989， 43（4）： 234-235.

序号	β	δ	SB-UB	SB
1	0	0.0	0.018	0.000
2	0	0.4	0.041	0.000
3	0	0.8	0.453	0.000
4	0	1.2	0.836	0.000
5	1	0.0	0.016	0.000
6	1	0.4	0.036	0.000
7	1	0.8	0.462	0.000
8	1	1.2	0.845	0.001
9	2	0.0	0.009	0.000
10	2	0.4	0.029	0.004
11	2	0.8	0.458	0.004
12	2	1.2	0.819	0.055

序号	β	δ	n=9	n=24	n=39
90	0	0.4	0.035	0.207	0.426
91	0	0.8	0.452	0.933	0.997
92	0	1.2	0.833	1.000	1.000
93	1	0.0	0.018	0.022	0.045
94	1	0.4	0.039	0.212	0.413
95	1	0.8	0.438	0.93	0.998
96	1	1.2	0.844	0.999	1.000
97	2	0.0	0.013	0.027	0.034
98	2	0.4	0.031	0.200	0.409
99	2	0.8	0.473	0.940	0.991
100	2	1.2	0.837	1.000	1.000

序号	n_s =1	n_s =2	n_s = 3	n_s =4	n_s =5	n_s =6
90	0.043	0.075	0.116	0.103	0.127	0.119
91	0.447	0.629	0.631	0.673	0.67	0.657
92	0.826	0.889	0.905	0.924	0.922	0.938
93	0.018	0.037	0.064	0.057	0.061	0.062
94	0.032	0.092	0.107	0.129	0.151	0.138
95	0.45	0.592	0.631	0.679	0.638	0.672
96	0.829	0.867	0.904	0.908	0.925	0.935
97	0.016	0.041	0.035	0.046	0.044	0.058
98	0.029	0.081	0.099	0.128	0.127	0.121
99	0.449	0.582	0.616	0.641	0.675	0.693
100	0.821	0.895	0.902	0.914	0.939	0.943

序号	S₁	S₂	S₃	S₄	S₅	S₆	S₇
90	0.205	0.483	0.185	0.090	0.073	0.353	0.287
91	0.931	0.978	0.930	0.516	0.493	0.899	0.868
92	1.000	1.000	1.000	0.850	0.869	0.992	0.975
93	0.034	0.115	0.032	0.090	0.118	0.116	0.079
94	0.210	0.518	0.239	0.070	0.093	0.383	0.259
95	0.918	0.979	0.922	0.514	0.533	0.913	0.869
96	1.000	1.000	1.000	0.878	0.880	0.993	0.983
97	0.028	0.089	0.038	0.092	0.095	0.098	0.057
98	0.201	0.460	0.196	0.082	0.085	0.342	0.286
99	0.932	0.985	0.951	0.520	0.516	0.885	0.851
100	0.999	1.000	1.000	0.867	0.877	0.984	0.970

[1]	夏德建, 王勇, 石国强. 自建VS.并购:物流一体化竞争下的电商平台演化博弈[J]. 中国管理科学, 2020, 28(4): 122-130.
[2]	温小琴, 胡奇英. 基于上游成员的机会成本和消费者偏好的供应链产品策略[J]. 中国管理科学, 2018, 26(6): 62-71.
[3]	陈占夺, 秦学志. 基于博弈的“外包内做”型制造外包违规控制研究[J]. 中国管理科学, 2016, 24(6): 78-89.
[4]	姚铮, 马超群, 杨智. 新产品开发网络资源与技术资源匹配关系:基于中国制造业企业的实证研究[J]. 中国管理科学, 2016, 24(4): 148-158.
[5]	李伟, 李敏强, 陈富赞. 两阶段软件发布管理中的最优质量与定价——顾客需求不确定条件下的分析[J]. 中国管理科学, 2015, 23(2): 108-115.
[6]	邱甲贤, 林漳希, 童牧. 第三方电子交易平台运营初期的定价策略——基于在线个人借贷市场的实证研究[J]. 中国管理科学, 2014, 22(9): 57-65.
[7]	段永瑞, 李贵萍, 霍佳震. 有限时域内部分缺货的变质品生产-定价策略研究[J]. 中国管理科学, 2014, 22(1): 94-103.
[8]	巩永华, 李帮义. 非线性需求下具有网络外部性的二级歧视定价研究[J]. 中国管理科学, 2010, 18(1): 102-106.
[9]	鲁文龙, 陈宏民. R&D合作与政府最优政策博弈分析[J]. 中国管理科学, 2003, (1): 60-62.