工作流程在時程上的管理上是一個很重要的議題，工作時程中異常的延遲時間將導致企業營運不彰，使得企業無法發揮最大的績效。因此本研究提出挖掘特例工作時程的演算法，根據過去工作時程記錄找出工作流程上異常延遲時間的活動，作為日後調整工作流程的參考依據。在管理上的意涵能輔助企業主管或顧問找出企業流程當中各個活動延遲的可能，透過改善以利日後有效控制特例的情況，另一方面則是可以方便管理者找出工作流程中時間異常的癥結點。
本研究中以活動為基礎，提出目前工作流程延遲時間最完整的可量化測量種類探討，而在演算法的設計部分則使用三維陣列存放方式，讓延遲時間計算上更有效率，並透過真實的資料所得到的實驗結果，提供管理者改善的方向。

The concept of workflow is an critical issue in time management. Irrational delay time not only causes a firm’s inefficient operations but also hinder a firm’s ability to optimize performance. This research provides an algorithm which based on workflow’s abnormal delay time. By finding out company’s workflow outlier and take it as a reference for adjusting the whole workflow, the algorithm presented in this research helps managers and consultants recognize all possible delay types of workflow’s activities as well as figure out the crucial activity of irregular instances of workflow easily. Building on the activity-based method, we explore possible types of workflow delay time and further propose complete uantifiable measurements. Three-dimension data store on struct is applied in the algorithm to compute time delay effectively. Besides, empirical data are drawn to validate our model as to provide practitioners additional instructions to improve operational performance.

[1] Hollingsworth D., "Workflow Management Coalition: the Workflow Reference Model", TC00-1003, 1995.
[2] Jorge Cardoso, Amit P. Sheth, and John Miller, "Workflow Quality of Service", presented at the Proceedings of the IFIP TC5/WG5.12 International Conference on Enterprise Integration and Modeling Technique: Enterprise Inter- and Intra-Organizational Integration: Building International Consensus, 2003
[3] James G. Kobielus, Workflow Strategies. (IDG Books Worldwide, Inc., 1997).
[4] Zhiping Walter Jeffrey L. Rummel, Rajiv Dewan and Abraham Seidmann, "Activity consolidation to improve responsiveness", European Journal of Operational Research, Vol 161 (3), pp. 683-703, 2005.
[5] Anthony J. Bonner, "Workflow, transactions and datalog", presented at the Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, 1999
[6] Hasan Davulcu, Michael Kifer, C. R. Ramakrishnan, and I. V. Ramakrishnan, "Logic based modeling and analysis of workflows", presented at the Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems, 1998
[7] Dirk Wodtke and Gerhard Weikum, "A Formal Foundation for Distributed Workflow Execution Based on State Charts", presented at 73 the Proceedings of the 6th International Conference on Database Theory, 1997
[8] Dirk Wodtke, Jeanine Wei, enfels, Gerhard Weikum, and Angelika Kotz Dittrich, "The Mentor Project: Steps Toward Enterprise-Wide Workflow Management", presented at the Proceedings of the Twelfth International Conference on Data Engineering, 1996
[9] Munindar P Singh, "Semantical considerations on workflows: An algebra for intertask dependencies", In Proc. of the Workshop on Database Programming Languages, pp. 6-8, 1995.
[10] W.M.P. van der Aalst, "The application of petri nets to worflow management", Circuits, Systems, and Computers, Vol 8, pp. 21–66, 1998.
[11] Gianluigi Greco, Antonella Guzzo, Giuseppe Manco, and Domenico Saccà, "Mining unconnected patterns in workflows", Information Systems Vol 32 (5), pp. 685-712, 2007.
[12] R. Agrawal and R. Srikant, "Fast Algorithms for Mining Association Rules", presented at the Conference on Very Large Databases, 1994
[13] Jiawei Han, Jian Pei, Yiwen Yin, and Runying Mao, "Mining Frequent Patterns without Candidate Generation: A Frequent-Pattern Tree Approach", Data Min. Knowl. Discov., Vol 8 (1), pp. 53-87, 2004.
[14] J. Pei, J. Han, B. Mortazavi-Asl, H. Pinto, Q. Chen, U. Dayal, and M. Hsu, "Prefixspan: Mining sequential patterns by prefix-projected growth", presented at the IEEE International Conference on Data Mining, 2001
[15] J. Han J. Pei, H. Lu, S. Nishio, S. Tang, and D. Yang, "H-Mine: 74 Hyper-structure mining of frequent patterns", presented at the IEEE International Conference on Data Mining, 2001 [16] T. Washi A. Inokuchi, and H. Motoda, "An Apriori-Based Algorithm for Mining Frequent Substructures from Graph Data", 4th European on Principles of Data Mining and Knowledge Discovery, pp. 13–23, 2000.
[17] Luc Dehaspe and Hannu Toivonen, "Discovery of frequent DATALOG patterns", Data Min. Knowl. Discov., Vol 3 (1), pp. 7-36, 1999.
[18] Akihiro and Washio Inokuchi, Takashi and Motoda, Hiroshi "An a priori-based algorithm for mining frequent substructures from graph data ", presented at the 4th European Conference on Principles and Practice of Knowledge Discovery in Databases, 2000
[19] Akihiro Inokuchi, Takashi Washio, and Hiroshi Motoda, "Complete Mining of Frequent Patterns from Graphs: Mining Graph Data", Mach. Learn., Vol 50 (3), pp. 321-354, 2003.
[20] Michihiro Kuramochi and George Karypis, "Frequent Subgraph Discovery", presented at the Proceedings of the 2001 IEEE International Conference on Data Mining, 2001
[21] Xifeng Yan and Jiawei Han, "gSpan: Graph-Based Substructure Pattern Mining", presented at the Proceedings of the 2002 IEEE International Conference on Data Mining, 2002
[22] J. Huan, W. Wang, and J. Prins, "Efficient mining of frequent subgraph in the presence of isomorphism", presented at the IEEE International Conference on Data Mining, 2003
[23] Xifeng Yan and Jiawei Han, "CloseGraph: mining closed frequent 75 graph patterns", presented at the Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, 2003
[24] Siegfried Nijssen and Joost N. Kok, "A quickstart in frequent structure mining can make a difference", presented at the Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining, 2004
[25] D. Cook L. Holder, and S. Djoko, "Substructure discovery in the SUBDUE system", In Proc. of the Workshop on Knowledge Discovery in Databases, pp. 169–180, 1994.
[26] C.-W. K. Chen and D. Y. Y. Yun, "Unifying graph matching problem with a practical solution", presented at the In Proceedings of International Conference on Systems, Signals, Control, Computers, 1998
[27] K. Yoshida and H. Motoda, "CLIP: Concept learning from inference patterns", Artificial Intelligence, pp. 63 92, 1995.
[28] H. K¨alvi¨ainen and E. Oja, "Comparisons of attributed graph matching algorithms for computer vision", In Proc. of STEP-90, Finnish Artificial Intelligence Symposium, pp. 354–368, 1990.
[29] D. A. L. Piriyakumar and P. Levi, "An efficient A* based algorithm for optimal graph matching applied to computer vision", In GRWSIA-98, 1998.
[30]V. A. Cicirello, "Intelligent retrieval of solid models", Master’s thesis, Drexel University, Philadelphia,PA, 1999.
[31] D. Dupplaw and P. H. Lewis, "Content-based image retrieval with scale-spaced object trees", presented at the Proc. of SPIE: Storage 76 and Retrieval for Media Databases, 2000
[32] H. Toivonen L. Dehaspe, and R. D. King, "Finding frequent substructures in chemical compounds", presente at the Proc. of the 4th International Conference on Knowledge Discovery and Data Mining, 1998
[33] A. Srinivasan, R. D. King, S. H. Muggleton, and M. Sternberg, "The predictive toxicology evaluation challenge", presented at the In Proc. of the 15th International Joint Conference on Artificial Intelligence (IJCAI), 1997
[34] Hawkins, Identification of outliers. (London:Chapman & Hall, 1980).
[35] Zengyou He, Xiaofei Xu, Joshua Zhexue Huang, and Shengchun Deng, "Mining class outliers: concepts, algorithms and applications in CRM", Expert Syst Appl, Vol 27 (4), pp. 681-697, 2004.
[36] Maneesh K. Singh and Narendra Ahuja, "Mean-Shift Segmentation with Wavelet-based Bandwidth Selection", presented at the Proceedings of the Sixth IEEE Workshop on Applications of Computer Vision, 2002
[37] R. J. Beckman and R. D. Cook, "Outlier.s", Technometrics, Vol 25, pp. 119-163, 1983.
[38] J. F. Gentleman and M. B. Wilk, "Detecting Outliers in a Two-Way Table: I. Statistical Behavior of Residuals", Technometrics, Vol 17, pp. 1-14, 1975.
[39] Mervyn G. Marasinghe, "A Multistage Procedure for Detecting Several Outliers in Linear Regression", Technometrics, Vol 27, pp. 395-399, 1985. 77
[40] Bernard Rosner, "Percentage Points for a Generalized ESD Many-Outlier Procedure", Technometrics, Vol 25, pp. 165-172 1983.
[41] S. R. Paul and Karen Y. Fung, "A Generalized Extreme Studentized Residual Multiple-Outlier-Detection Procedure in Linear Regression", Technometrics, Vol 33, pp. 339-348, 1991.
[42] Kenji Yamanishi, Jun-Ichi Takeuchi, Graham Williams, and Peter Milne, "On-Line Unsupervised Outlier Detection Using Finite Mixtures with Discounting Learning Algorithms", Data Min. Knowl. Discov., Vol 8 (3), pp. 275-300, 2004.
[43] Kenji Yamanishi and Jun-ichi Takeuchi, "Discovering outlier filtering rules from unlabeled data: combining a supervised learner with an unsupervised learner", presented at the Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining, 2001
[44] Kenji Yamanishi and Jun-ichi Takeuchi, "A unifying framework for detecting outliers and change points from non-stationary time series data", presented at the Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining, 2002
[45] Tukey J W, Exploratory Data Analysis. (1994).
[46]Franco P. Preparata and Michael I. Shamos, Computational geometry: an introduction. (Springer-Verlag New York, Inc., 1985).
[47] Struyf A and Rousseeuw P J, "High-dimensional computation of the deepest location", Computational Statistics & Data Analysis, Vol 34 (4), pp. 415-426, 2000.
[48] Ida Ruts and Peter J. Rousseeuw, "Computing depth contours of 78 bivariate point clouds", Comput. Stat. Data Anal., Vol 23 (1), pp. 153-168, 1996.
[49] Arning A, Agrawal R, and Raghavan P, "A Linear Method for DeviationDetection in Large Database", presented at the DataMining and Knowledge( Special Issue on High Performance Data Mining) 1996
[50] Sunita Sarawagi, Rakesh Agrawal, and Nimrod Megiddo, "Discovery-Driven Exploration of OLAP Data Cubes", presented at the Proceedings of the 6th International Conference on Extending Database Technology: Advances in Database Technology, 1998
[51] H. V. Jagadish, Nick Koudas, and S. Muthukrishnan, "Mining Deviants in a Time Series Database", presented at the Proceedings of the 25th International Conference on Very Large Data Bases, 1999[52] Edwin M. Knorr and Raymond T. Ng, " A Unified Notion of Outliers: Properties and Computation ", presented at the In Proc. of the International Conference on Knowledge Discovery and Data Mining, 1997
[53] E. Knorr, & Ng, R., "Finding intentional knowledge of distance-based outliers", VLDB99, pp. 211–222, 1999.
[54] Sridhar Ramaswamy, Rajeev Rastogi, and Kyuseok Shim, "Efficient algorithms for mining outliers from large data sets", presented at the Proceedings of the 2000 ACM SIGMOD international conference on Management of data, 2000
[55] Fabrizio Angiulli and Clara Pizzuti, "Fast Outlier Detection in High Dimensional Spaces", presented at the Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge 79 Discovery, 2002
[56] Micheline Kamber Jiawei Han, Data mining: concepts and techniques. (Morgan Kaufmann, 2006).
[57] Stephen D. Bay and Mark Schwabacher, "Mining distance based outliers in near linear time with randomization and a simple pruning rule", presented at the Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, 2003
[58] Norio Katayama and Shin''ichi Satoh, "The SR-tree: an index structure for high-dimensional nearest neighbor queries", presented at the Proceedings of the 1997 ACM SIGMOD international conference on Management of data, 1997
[59] Rakesh Agrawal, Johannes Gehrke, Dimitrios Gunopulos, and Prabhakar Raghavan, "Automatic subspace clustering of high dimensional data for data mining applications", presented at the Proceedings of the 1998 ACM SIGMOD international conference on Management of data, 1998
[60] Charu C. Aggarwal and Philip S. Yu, "Finding generalized projected clusters in high dimensional spaces", presented at the Proceedings of the 2000 ACM SIGMOD international conference on Management of data, 2000
[61] Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, and Jorg Sander, "OPTICS-OF: Identifying Local Outliers", 1999
[62] Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng, J, and rg Sander, "LOF: identifying density-based local outliers", SIGMOD Rec., Vol 29 (2), pp. 93-104, 2000. 80
[63] Jian Tang, Zhixiang Chen, Ada Wai-Chee Fu, and David Wai-Lok Cheung, "Enhancing Effectiveness of Outlier Detections for Low Density Patterns", presented at the Proceedings of the 6th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining, 2002
[64] A.L.M. Chiu and Ada Wai-chee Fu, "Enhancements on local outlier detection", IDEAS03, pp. 298- 307, 2003.
[65] Ravindra N. Chittimoori, Lawrence B. Holder, and Diane J. Cook, "Applying the Subdue Substructure Discovery System to the Chemical Toxicity Domain", presented at the Proceedings of the Twelfth International Florida Artificial Intelligence Research Society Conference, 1999