﻿ 基于PLS回归的单箱消耗影响因素分析—来自红河卷烟厂卷包过程中的烟丝消耗控制数据 The Analysis of Influence Factors of Single Box Consumption Based on the PLS Regression—From the Data of Tobacco Consumption Control in Honghe Cigarette Factory

Statistical and Application
Vol.04 No.03(2015), Article ID:15996,11 pages
10.12677/SA.2015.43016

The Analysis of Influence Factors of Single Box Consumption Based on the PLS Regression

—From the Data of Tobacco Consumption Control in Honghe Cigarette Factory

Lei Xu1*, Xingxu Li1, Yan Zhang2, Wenneng Li2, Bo Zhang2

1School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming Yunnan

2Honghe Cigarette Factory, Hongyun Honghe Group, Honghe Yunnan

*通讯作者。

Email: *xulei-2008@163.com

Received: Aug. 16th, 2015; accepted: Aug. 31th, 2015; published: Sep. 7th, 2015

ABSTRACT

On the basis of some conditions for the application of partial least squares regression analysis and multivariate linear regression analysis in this paper, we can conclude that partial least squares regression (PLS) can effectively improve multicollinearity of variables. When the sample size is less than the number of variables, it also can be used to do regression modeling. Then, from 12 groups of sample data of Tobacco consumption control in Honghe Cigarette Factory, we have analyzed and compared the results of partial least squares regression modeling and multivariate linear regression modeling in the paper. It has shown that the significant factors affecting the single box consumption are single case of Wasting, single case of Running, single case of Packet rejection and single case of Short excluded volume. Therefore, the work of the cigarette factory in the process of reducing the cost should be firstly controlling these four single box loss indicators, so that we will achieve the immediate results.

Keywords:Single Box Consumption, Influence Factors, PLS Regression, Comparative Analysis

—来自红河卷烟厂卷包过程中的烟丝消耗控制数据

1云南财经大学统计与数学学院，云南 昆明

2红云红河烟草(集团)有限责任公司红河卷烟厂，云南 红河

Email: *xulei-2008@163.com

1. 引言

2. 统计分析方法的选择

2.1. 多元线性回归

2.2. 偏最小二乘回归(PLS)

3. 实证分析和结果的比较

3.1. 数据的来源及变量的选取

3.2. 相关性分析

Figure 1. Chart: production consumption tracking survey

Table 1. The data table of single box consumption in the process of winding

Table 2. Correlation coefficient matrix of single box indexes

3.3. 偏最小二乘回归建模

3.3.1. 选取主成分

Figure 2. Chart: selecting the principal component of independent variables

3.3.2. 拟合偏最小二乘回归模型

3.3.3. 检验所建模型的残差

3.4. 多元线性回归建模

Table 3. The table of ANOVA

Table 4. The table of coefficient of model independent variable and standard coefficient

Figure 3. Chart: normality of residuals

3.4.1. 拟合多元线性回归模型

3.4.2. 检验模型的残差

3.5. 两种建模结果的比较

3.5.1. 对比模型方程

Table 5. The table of ANOVA

Table 6. The table of coefficient of model independent variable

3.5.2. 预测误差平方和(PRESS)

PRESS类似于误差平方和(SSE)，是预测误差的平方和，用于评估模型的预测能力。一般而言，PRESS值越小，模型的预测能力越强。

4. 结论

1) 不仅各个单箱损耗指标和成品丝含水率与单箱烟丝消耗存在统计意义上的显著相关关系，并且这几个损耗指标之间也存在统计意义上显著的相关关系。因此，卷烟厂要想降低其单箱烟丝消耗水平不能只管控某一项单箱损耗指标，应当从卷包生产过程的全局进行考虑。

2) 成品丝含水率不仅对单箱烟丝消耗具有一定的负向影响，而且与大部分单箱损耗指标之间存在一定的负相关关系。这说明成品丝含水率在卷包生产过程中的降耗工作中有着重要的作用，应当给予重点关注。

3) 由偏最小二乘回归模型的结果可知，单箱废烟、单箱跑条、单箱小包机剔除和单箱空头剔除这四个变量对因变量单箱耗丝具有显著性影响。因此，卷烟厂在卷包过程中的降耗工作应当首先从控制这四个单箱损耗指标开始实施，才能取得立竿见影的效果。

4) 通过比较偏最小二乘模型和多元线性回归模型所得的结果，可以认为偏最小二乘回归模型更适合于分析这种样本少、变量多的样本数据，尤其是所研究自变量个数多于样本量的情况。而在工业生产的过程中，因各种原因导致测试所采集的数据量较少和研究的指标变量较多的情况屡见不鲜，因此采用偏最小二乘回归分析建模更符合实际工作和研究的需要，值得深入学习和推广。

The Analysis of Influence Factors of Single Box Consumption Based on the PLS Regression—From the Data of Tobacco Consumption Control in Honghe Cigarette Factory[J]. 统计学与应用, 2015, 04(03): 144-154. http://dx.doi.org/10.12677/SA.2015.43016

1. 1. 贺万华, 曹兴洪, 等 (2007) 卷烟制丝和卷制过程中主要质量指标与消耗指标的关系及评价方法. 中国烟草学报, 5, 17-22.

2. 2. 汪涛, 张琦 (2011) 利用主成分分析和正交试验解决卷烟加工中的原料消耗问题. 黑龙江科技信息, 5, 50.

3. 3. 何晓群, 刘文卿 (2007) 应用回归分析. 中国人民大学出版社, 北京.

4. 4. Wold, H. (1975) Soft modelling by latent variables: The non-linear iterative partial least squares (NIPALS) approach. Perspectives in proba-bility and statistics. Papers in Honour of M. S. Bartlett. Academic Press, London, 117-142.

5. 5. 王惠文 (1999) 偏最小二乘回归方法及应用. 国防工业出版社, 北京.