A Method Of Grouping And Ranking Based On Shewhart Control Charts And DEA Cross-efficiency

In the context of high quality economy,the role of quality in promoting economic development is becoming more and more obvious,quality is getting more and more attention,and theories and methods of quality management are becoming more and more popular and widely used.Performance and its evaluation is a common topic of concern nowadays.Performance is a comprehensive reflection of various aspects of work and is composed of a series of indicators,and at the same time,in order to improve the accuracy of performance evaluation,the indicators composed of performance evaluation should reflect the inherent characteristics of the performance evaluation object,so performance and its evaluation is a multiindicator quality problem.The most commonly used method for multiindicator performance evaluation problem is DEA.Based on the unconventional phenomenon that the order of CCR model effective DMUs are located after non-effective DMUs in the ranking of DMUs in the DEA evaluation system,we firstly put forward the necessity of homogeneity research on DMUs through relevant literature combing,and then implement the definition of DMU homogeneity,refine the influencing factors of DMU homogeneity and its mechanism of action analysis.Second,for the current DMU grouping using the effective DMU as a group and non-effective DMU as another group lack of theoretical basis and persuasive problems.Based on the fluctuation concept of quality management,DMU grouping should be carried out based on the idea of"homogeneous within groups and heterogeneous between groups",based on this idea,the specific method of this paper is to design the grouping line for DMU grouping based on the DEA cross-efficiency,using the Shewhart control chart,dividing the process into two states of controlled inside the line and uncontrolled outside the line based on the control line,the grouping criterion of DMU grouping is formed,and all DMUs composing the DEA evaluation system are divided into two groups:(located in the grouping line)most of the non-effective DMUs in CCR model as group A,and the effective DMUs in CCR model and(located outside the grouping line)some non-effective DMUs as group B.The grouping is homogeneous within the group and heterogeneous between the groups,and on this basis the sorting is implemented by group,so that the DMU grouping has its the theoretical basis and the basic assumptions for the evaluation of DEA evaluation system are satisfied when ranking.This group ranking method reduces the risk that the order of non-valid DMUs is located before valid DMUs to a certain extent because group B contains fewer non-valid DMUs.At the same time,in order to improve the utilization rate of data and the continuity of the analysis and evaluation process,and to reduce the workload of unnecessary repeated calculations,the intra-group ranking of the group formed by CCR model effective DMUs and the least non-effective DMUs is not re-ordered by measuring the cross-efficiency based on the determination of weights based on CCR-DEA,but directly after directly deleting the data of another group of non-effective DMUs with the intermediate data at the time of grouping.The DMUs are reordered by the average cross-efficiency.To verify the rationality of the above grouping ranking method and distinguish the role of different cross-efficiencies,the paper further applies the TOPSIS ranking method by measuring the positive and negative ideal solutions when evaluating cross-efficiencies,constituting a ranking vector to form a TOPSIS-DEA cross-efficiency ranking model and implementing the ranking by group,which also has the same effect.Finally,the method of this paper is applied to robot evaluation for case analysis,and the results of the case show that the cross-efficiency of CCR model effective DMUs and some non-effective DMUs fall outside the grouping line,indicating that CCR model effective DMUs and some noneffective DMUs have homogeneity,which further indicates that the grouping cannot simply take CCR model effective DMUs as one group and all non-effective DMUs as another group,otherwise,non-valid DMU groups still do not meet the basic prerequisites of a homogeneous DEA evaluation system.At the same time,the ranking based on grouping has the feature that all CCR model effective DMUs are in front of non-effective DMUs,which in a certain sense solves the unconventional phenomenon that the order of CCR model effective DMUs is behind non-effective DMUs in the current DEA cross-efficiency evaluation,further demonstrating the necessity and feasibility of DMU grouping ranking and feasibility,and verifies the rationality and feasibility of the method in this paper.The conclusions of this paper mainly include:(1)MIMO’s DMU in the implementation of DEA performance evaluation and ranking,should be established under the basic assumptions of homogeneous DMU premise,reasonable selection of DMU,so as to constitute a homogeneous DMU composition of the DEA evaluation system,if necessary,DMU homogeneity analysis evaluation(to carry out homogeneity test);(2)There are homogeneous and non-homogeneous problems among DMUs,whose influencing factors can be refined into 5M1E,whose mechanism of action is a small difference and a large difference in influencing factors,specifically in terms of cross-efficiency located in different regions of the control chart;(3)For DMUs in a DEA evaluation system,there is also homogeneity between CCR model effective DMUs and some non-effective DMUs,and the grouping cannot be simply based on whether the DMUs are effective,but should be based on their cross-efficiency falling in specific region of the control chart;(4)The ranking based on grouping helps to improve the credibility of the ranking results.