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Detecting Process Duration Drift Using Gamma Mixture Models in a Left-Truncated and Right-Censored Environment
Open accessAbstract
Within the realm of business context, process duration signifies time spent by customers between successive activities. This temporal perspective offers important insight to customer behavior, highlighting potential bottlenecks, and influencing business management decisions. The distribution of these process duration often changes over time due to factors such as seasonality, emerging legislation, changes to supply chains, and customer demand. Referred to as concept drift, these variations pose challenges for robust process modeling, understanding, and refinement. Subsequently, gamma mixture models are widely employed to model durations. These source data can, however, become left-truncated and right-censored within any specific observation window thereby necessitating a (well-known) modification to the likelihood function. The approach reported in this article leveraged this adapted likelihood across a series of observation windows, applying the likelihood ratio test to identify duration changes/concept drift. Due to its flexibility in modelling any duration distribution, the gamma mixture model was used with Nelder–Mead optimized likelihood for the left-truncated and right-censored data. The number of gamma components was determined by the Bayesian information criterion. The proposed framework underwent validation through simulated exponential samples, leading to recommendations for its practical application. Subsequently, we applied the methodology to three real-life event logs exhibiting diverse characteristics. Experimental results showcase the effectiveness of our approach in terms of data fitting, as compared to Kaplan–Meier curves, and in detecting instances of drift. This comprehensive validation underscores the practical utility and reliability of our framework for dynamic business scenarios.
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Citations
Cites
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
Lagarias, J. C., Reeds, J. A., Wright, M. H., & Wright, P. E. (1998) · SIAM Journal on Optimization · doi:10.1137/s1052623496303470 · Cited by 7,449
The EM Algorithm and Extensions
Kushary, D., McLachlan, G. J., & Krishnan, T. (1998) · Technometrics · doi:10.2307/1271189 · Cited by 5,419
How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis
Fraley, C. (1998) · The Computer Journal · doi:10.1093/comjnl/41.8.578 · Cited by 2,549
Klein, J. P., & Moeschberger, M. L. (2003) · Statistics for biology and health · doi:10.1007/b97377 · Cited by 1,832
Continuous Univariate Distributions.
Chatfield, C., Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348907 · Cited by 1,008
Christophe Biernacki, A., Celeux, G., & Govaert, G. (2003) · Computational Statistics & Data Analysis · doi:10.1016/s0167-9473(02)00163-9 · Cited by 657
van der Aalst, W. M. P. (2012) · ACM Transactions on Management Information Systems · doi:10.1145/2229156.2229157 · Cited by 544
Stochastic Models. An Algorithmic Approach.
PE, & Tijms, H. C. (1995) · Journal of the American Statistical Association · doi:10.2307/2291554 · Cited by 359
Lee, C., Yoon, J., & van der Schaar, M. (2019) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2019.2909027 · Cited by 338
(2006) · DergiPark (Istanbul University) · Cited by 315
The Time Value of Ruin in a Sparre Andersen Model
Gerber, H. U., & Shiu, E. S. W. (2005) · North American Actuarial Journal · doi:10.1080/10920277.2005.10596197 · Cited by 255
Schmid, C. H., Lau, J., McIntosh, M. W., & Cappelleri, J. C. (1998) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19980915)17:17 · Cited by 211
Cain, K. C., Harlow, S. D., Little, R. J. A., Nan, B., Yosef, M., Taffe, J. R., & Elliott, M. R. (2011) · American Journal of Epidemiology · doi:10.1093/aje/kwq481 · Cited by 208
Dealing With Concept Drifts in Process Mining
Bose, R. P. J. C., van der Aalst, W. M. P., Žliobaitė, I., & Pechenizkiy, M. (2013) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2013.2278313 · Cited by 192
An Introduction to Survival Statistics: Kaplan-Meier Analysis
Dudley, W. N., Rita Wickham, P., & Coombs, N. C. (2016) · Journal of the Advanced Practitioner in Oncology · doi:10.6004/jadpro.2016.7.1.8 · Cited by 175
COVID19: an announced pandemic
Platto, S., Xue, T., & Carafoli, E. (2020) · Cell Death and Disease · doi:10.1038/s41419-020-02995-9 · Cited by 134
A Survey on Concept Drift in Process Mining
Sato, D. M. V., de Freitas, S. C., Barddal, J. P., & Scalabrin, E. E. (2021) · ACM Computing Surveys · doi:10.1145/3472752 · Cited by 123
Abdel‐Basset, M., Mohamed, R., & Mirjalili, S. (2020) · Knowledge-Based Systems · doi:10.1016/j.knosys.2020.106619 · Cited by 109
Detecting Sudden and Gradual Drifts in Business Processes from Execution Traces
Maaradji, A., Dumas, M., Rosa, M. L., & Ostovar, A. (2017) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2017.2720601 · Cited by 108
An introduction to finite mixture distributions
Everitt, B. S. (1996) · Statistical Methods in Medical Research · doi:10.1177/096228029600500202 · Cited by 100
Data-Driven Process Discovery - Revealing Conditional Infrequent Behavior from Event Logs
Mannhardt, F., de Leoni, M., Reijers, H. A., et al. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-59536-8_34 · Cited by 99
Detecting sudden and gradual drifts in business processes from execution traces
Maaradji, A., Dumas-Menijvar, M., Rosa, M. L., & Ostovar, A. (2017) · QUT ePrints (Queensland University of Technology) · Cited by 94
Anomaly detection in business processes using process mining and fuzzy association rule learning
Sarno, R., Sinaga, F., & Sungkono, K. R. (2020) · Journal Of Big Data · doi:10.1186/s40537-019-0277-1 · Cited by 90
Gormley, I. C., Murphy, T. B., & Raftery, A. E. (2022) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-033121-115326 · Cited by 74
FITTING MIXTURES OF ERLANGS TO CENSORED AND TRUNCATED DATA USING THE EM ALGORITHM
Verbelen, R., Gong, L., Antonio, K., Badescu, A. L., & Lin, S. (2015) · Astin Bulletin · doi:10.1017/asb.2015.15 · Cited by 73
Change Point Detection and Dealing with Gradual and Multi-order Dynamics in Process Mining
Martjushev, J., Bose, R. P. J. C., & van der Aalst, W. M. P. (2015) · Lecture notes in business information processing · doi:10.1007/978-3-319-21915-8_11 · Cited by 62
k-Sample tests based on the likelihood ratio
Zhang, J., & Wu, Y. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2006.08.029 · Cited by 56
Chebyshev polynomials, moment matching, and optimal estimation of the unseen
Wu, Y., & Yang, P. (2019) · The Annals of Statistics · doi:10.1214/17-aos1665 · Cited by 55
On modeling left-truncated loss data using mixtures of distributions
Blostein, M., & Miljkovic, T. (2018) · Insurance Mathematics and Economics · doi:10.1016/j.insmatheco.2018.12.001 · Cited by 48
Efficient fitting of long-tailed data sets into hyperexponential distributions
Riska, A., Diev, V., & Evgenia Smirni, A. (2003) · Globecom · doi:10.1109/glocom.2002.1189083 · Cited by 47
Evaluation Goals for Online Process Mining: A Concept Drift Perspective
Ceravolo, P., Tavares, G. M., Barbon, S., & Damiani, E. (2020) · IEEE Transactions on Services Computing · doi:10.1109/tsc.2020.3004532 · Cited by 47
Cluster-based fitting of phase-type distributions to empirical data
Reinecke, P., Krauß, T., & Wolter, K. (2012) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2012.03.016 · Cited by 45
Detecting Concept Drift in Processes using Graph Metrics on Process Graphs
Seeliger, A., Nolle, T., & Mühlhäuser, M. (2017) · doi:10.1145/3040565.3040566 · Cited by 44
Multi-perspective Comparison of Business Process Variants Based on Event Logs
Nguyen, H. H., Dumas, M., Rosa, M. L., & ter Hofstede, A. H. M. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-00847-5_32 · Cited by 44
Explainable concept drift in process mining
Adams, J. N., van Zelst, S. J., Rose, T., et al. (2023) · Information Systems · doi:10.1016/j.is.2023.102177 · Cited by 43
Proceedings of the 2003 international conference on Business process management
van der Aalst, W. M. P., ter Hofstede, A. H. M., & Weske, M. (2003) · Cited by 42
A Framework for Explainable Concept Drift Detection in Process Mining
Adams, J. N., van Zelst, S. J., Quack, L., et al. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-85469-0_25 · Cited by 35
Family of generalized gamma distributions: Properties and applications
Alzaatreh, A., Soyadı, Y. A. Y., Lee, C., et al. (2015) · Hacettepe Journal of Mathematics and Statistics · doi:10.15672/hjms.20156610980 · Cited by 30
Finding Process Variants in Event Logs
Bolt, A., van der Aalst, W. M. P., & de Leoni, M. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-69462-7_4 · Cited by 28
A Flexible Parametric Modelling Framework for Survival Analysis
Burke, K., Jones, M. C., & Noufaily, A. (2020) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12398 · Cited by 25
Self-citationAn Approach For Concept Drift Detection in a Graph Stream Using Discriminative Subgraphs
Paudel, R., & Eberle, W. (2020) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3406243 · Cited by 24
The state-of-the-art of business process mining challenges
R’bigui, H., bigui, N. A., & Cho, C. (2017) · International Journal of Business Process Integration and Management · doi:10.1504/ijbpim.2017.088819 · Cited by 24
Left‐truncated and right‐censored field failure data: Review of parametric analysis for reliability
Emura, T., & Michimae, H. (2022) · Quality and Reliability Engineering International · doi:10.1002/qre.3161 · Cited by 23
Estimation for Semi-Markov Manpower Models in a Stochastic Environment
McClean, S. I., & Montgomery, E. (1999) · Springer eBooks · doi:10.1007/978-1-4613-3288-6_13 · Cited by 21
Self-citationCONDA-PM—A Systematic Review and Framework for Concept Drift Analysis in Process Mining
Elkhawaga, G., Abu-Elkheir, M., Barakat, S., Riad, A. M., & Reichert, M. (2020) · Algorithms · doi:10.3390/a13070161 · Cited by 21
Quality-Informed Process Mining: A Case for Standardised Data Quality Annotations
Goel, K., Leemans, S. J. J., Martin, N., & Wynn, M. T. (2022) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3511707 · Cited by 20
Richter, F., & Seidl, T. (2018) · Information Systems · doi:10.1016/j.is.2018.11.003 · Cited by 19
Detecting and Identifying Data Drifts in Process Event Streams Based on Process Histories
Stertz, F., & Rinderle‐Ma, S. (2019) · Lecture notes in business information processing · doi:10.1007/978-3-030-21297-1_21 · Cited by 18
A Nonparametric Maximum Likelihood Estimator for Incomplete Renewal Data
McClean, S. I., & Devine, C. (1995) · Biometrika · doi:10.2307/2337345 · Cited by 14
Self-citationHidalgo, J. I. G., Santos, S. G. T. D. C., & de Barros, R. S. M. (2021) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3466616 · Cited by 13
Bayesian parametric models for survival prediction in medical applications
Paolucci, I., Lin, Y., Silva, J. A. M., Brock, K. K., & Odisio, B. C. (2023) · BMC Medical Research Methodology · doi:10.1186/s12874-023-02059-4 · Cited by 13
Log-location-scale-log-concave distributions for survival and reliability analysis
Jones, M. C., & Noufaily, A. (2015) · Electronic Journal of Statistics · doi:10.1214/15-ejs1089 · Cited by 12
Valeriano, K. A. L., Galarza, C. E., Matos, L. A., et al. (2023) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2023.105174 · Cited by 12
A multi-components approach to monitoring process structure and customer behaviour concept drift
Yang, L., McClean, S. I., Donnelly, M. P., Burke, K., & Khan, K. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.118533 · Cited by 11
Self-citationOn some stochastic comparisons of arithmetic and geometric mixture models
Shojaee, O., & Babanezhad, M. (2022) · Metrika · doi:10.1007/s00184-022-00880-3 · Cited by 11
Semi-Markov Models for Process Mining in Smart Homes
McClean, S. I., & Yang, L. (2023) · Mathematics · doi:10.3390/math11245001 · Cited by 11
Self-citationLearning correlations using the mixture-of-subsets model
Somaiya, M. H., Jermaine, C., & Ranka, S. (2008) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/1324172.1324175 · Cited by 7
Wu, K., Wang, L., Li, Y., et al. (2021) · Mathematics · doi:10.3390/math9212703 · Cited by 6
A hierarchical Bayesian analysis for bivariate Weibull distribution under left-censoring scheme
Peralta, D., de Oliveira, R. P., & Achcar, J. A. (2023) · Journal of Applied Statistics · doi:10.1080/02664763.2023.2235093 · Cited by 4
Research works printed but not linked: 6
- Sylvio Barbon Junior, Gabriel Marques Tavares, Victor G. Turrisi da Costa, Paolo Ceravolo, and Ernesto Damiani. 2018. A framework for human-in-the-loop monitoring of concept-drift detection in event log stream. In Proceedings of the Companion Proceedings of the The Web Conference (WWW ’18). 319–326.
- B. F. A. Hompes, J. C. A.M. Buijs, W. M. P. Van der Aalst, P. M. Dixit, and J. Buurman. 2015a. Discovering deviating cases and process variants using trace clustering. In Proceedings of the 27th Benelux Conference on Artificial Intelligence (BNAIC). 1–9.
- Bart Hompes, Joos C. A. M. Buijs, Wil M. P. van der Aalst, Prabhakar M. Dixit, and Hans Buurman. 2015b. Detecting change in processes using comparative trace clustering. In Proceedings of the 5th International Symposium on Data-Driven Process Discovery and Analysis. 95–108.
- Daniela Luengo and Marcos Sepúlveda. 2011. Applying clustering in process mining to find different versions of a business process that changes over time. In Proceedings of the International Conference on Business Process Management. Springer, 153–158.
- Yang Song, Conor Durkan, Iain Murray, and Stefano Ermon. 2021. Maximum likelihood training of score-based diffusion models. In Proceedings of the Advances in Neural Information Processing Systems, Vol. 34. 1415–1428.
- Wil Van Der Aalst, Arya Adriansyah, Ana Karla Alves De Medeiros, Franco Arcieri, Thomas Baier, Tobias Blickle, Jagadeesh Chandra Bose, Peter Van Den Brand, Ronald Brandtjen, Joos Buijs, Andrea Burattin, Josep Carmona, Malu Castellanos, Jan Claes, Jonathan Cook, Nicola Costantini, Francisco Curbera, Ernesto Damiani, Massimiliano de Leoni, Pavlos Delias, Boudewijn F. van Dongen, Marlon Dumas, Schahram Dustdar, Dirk Fahland, Diogo R. Ferreira, Walid Gaaloul, Frank van Geffen, Sukriti Goel, Christian Günther, Antonella Guzzo, Paul Harmon, Arthur ter Hofstede, John Hoogland, Jon Espen Ingvaldsen, Koki Kato, Rudolf Kuhn, Akhil Kumar, Marcello La Rosa, Fabrizio Maggi, Donato Malerba, Ronny S. Mans, Alberto Manuel, Martin McCreesh, Paola Mello, Jan Mendling, Marco Montali, Hamid R. Motahari-Nezhad, Michael zur Muehlen, Jorge Munoz-Gama, Luigi Pontieri, Joel Ribeiro, Anne Rozinat, Hugo Seguel Pérez, Ricardo Seguel Pérez, Marcos Sepúlveda, Jim Sinur, Pnina Soffer, Minseok Song, Alessandro Sperduti, Giovanni Stilo, Casper Stoel, Keith Swenson, Maurizio Talamo, Wei Tan, Chris Turner, Jan Vanthienen, George Varvaressos, Eric Verbeek, Marc Verdonk, Roberto Vigo, Jianmin Wang, Barbara Weber, Matthias Weidlich, Ton Weijters, Lijie Wen, Michael Westergaard, and Moe Wynn. 2011. Process mining manifesto. In Proceedings of the International Conference on Business Process Management. Springer, 169–194.
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Larger and more instructable language models become less reliable
Zhou, L., Schellaert, W., Martínez-Plumed, F., Moros-Daval, Y., Ferri, C., & Hernández-Orallo, J. (2024) · Nature · doi:10.1038/s41586-024-07930-y · Cited by 203
Metadata
- Authors
- Yang, L., McClean, S., Donnelly, M., Khan, K., & Burke, K.
- Affiliations
- University of Ulster (GB)
- BT Group (United Kingdom) (GB)
- University of Limerick (IE)
- Venue
- ACM Transactions on Knowledge Discovery from Data
- Published
- 2024-08-21
- Volume
- 18
- Issue
- 8
- Pages
- 1-24
- ISSN
- 1556-4681 (ISSN-L)
- 1556-472X
- OpenAlex
- W4399576866
- Cited by
- 9
- References
- 59
- Citations by year
- 2025: 5 · 2024: 4
- FWCI
- 4.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Transactions on Knowledge Discovery from Data (publishedVersion)
- Ulster University Research Portal (Ulster University) (acceptedVersion, other-oa)
- Funders
- British Telecom Ireland Innovation Center
- British Telecom and Invest Northern Ireland
- Topics
- Social Sciences › Business, Management and Accounting › Management Information Systems › Business Process Modeling and Analysis
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- concept drift detection, gamma mixture model, left-truncated data, right-censored data, likelihood ratio test, Nelder-Mead algorithm, Bayesian information criterion, event logs, process mining, duration modeling, business process monitoring
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