Modelling Patients Waiting and Service Time by ARIMA Model: A Case of Federal University Gusau Clinic

Authors

  • Aliyu Usman Moyi Department of Mathematics, Federal University Gusau, Nigeria
  • Kabir Bello Department of Mathematics, Federal University Gusau, Nigeria
  • Olayemi Joshua Ibidoja Department of Mathematics Federal University Gusau Nigeria https://orcid.org/0000-0003-4982-5209
  • Garba Muhammad Department of Mathematics, Federal University Gusau, Nigeria

Keywords:

Waiting Time, Service Time, ARIMA, Modelling, Outliers

Abstract

The ability to model and forecast waiting and service time to increase patients' satisfaction, reduce waiting time, avoid casualties, and increase efficiency in service delivery is crucial. It encourages the identification of future pressure by using the relevant key performance indicators. In this paper, the ARIMA model is used to study the waiting and service time of patients at the {\it Federal University Gusau} Health Services Clinic. The system was a single, time-independent arrival with many service points. Based on the results found in the waiting and service processes, the service time has a lower mean and variance when compared to the waiting time. The waiting time has a lower skewness and kurtosis when compared to the service time. The Ljung-Box (Q) Statistic test shows that the correlation in the time series has been adequately captured for the waiting and service time processes, though the waiting and service time processes have 4 and 10 outliers respectively. The ARIMA (0,1,2) and ARIMA (2,1,1) are selected for modelling the waiting and service time respectively based on the evaluation metrics.

Dimensions

D. Claudio, A. Miller & A. Huggins, ‘‘Time series forecasting in an outpatient cancer clinic using common-day clustering’’, IIE Trans. Healthc. Syst. Eng. 4 (2014) 16. https://doi.org/10.1080/19488300.2013.879459.

C. H. Cheng, J. W. Wang & C. H. Li, ‘‘Forecasting the number of outpatient visits using a new fuzzy time series based on weighted-transitional matrix’’, Expert Syst. Appl. 34 (2008) 2568. https://doi.org/10.1016/j.eswa.2007.04. 007.

R. Shumway & D. S. Stoffer, Time Series Analysis and Its Applications With R Examples’’, Springer, Cham, Switzerland, 2016. https://doi.org/10. 1007/978-3-319-52452-8.

L. Luo, L. Luo, X. Zhang & X. He, ‘‘Hospital daily outpatient visits forecasting using a combinatorial model based on ARIMA and SES models’’, BMC Health Serv. Res. 17 (2017) 469. https://doi.org/10.1186/ s12913-017-2407-9.

L. O’Brien-Pallas, A. Baumann, G. Donner, G. T. Murphy, J. LochhaasGerlach & M. Luba, ‘‘Forecasting models for human resources in health care’’, J. Adv. Nurs. 33 (2001) 120. https://doi.org/10.1046/j.1365-2648. 2001.01645.x.

J. W. Taylor, ‘‘Short-term electricity demand forecasting using double seasonal exponential smoothing’’, Journal of the Operational Research Society 54 (2003) 8. https://doi.org/10.1057/palgrave.jors.2601589.

M. Wagner, ‘‘Forecasting Daily Demand in Cash Supply Chains’’, American Journal of Economics and Business Administration 2 (2010) 4. https: //papers.ssrn.com/sol3/papers.cfm?abstract_id=2212817.

T. R. Willemain, C. N. Smart & H. F. Schwarz, ‘‘A new approach to forecasting intermittent demand for service parts inventories’’, Int. J. Forecast 20 (2004) 3. https://doi.org/10.1016/S0169-2070(03)00013-X.

M. Khashei & M. Bijari, ‘‘A new class of hybrid models for time series forecasting’’, Expert Syst Appl 39 (2012) 4. https://doi.org/10.1016/j.eswa. 2011.09.157.

Purwanto, C. Eswaran & R. Logeswaran, ‘‘A dual hybrid forecasting model for support of decision making in healthcare management’’, Advances in Engineering Software 53 (2012) 23. https://doi.org/10.1016/j.advengsoft. 2012.07.006.

H. Batal, J. Tench, S. Mcmillan, J. Adams & P. S. Mehler, ‘‘Predicting Patient Visits to an Urgent Care Clinic Using Calendar Variables’’, Academic Emergency Medicine 8 (2001) 1. https://doi.org/10.1111/j.1553-2712. 2001.tb00550.x

S. S. Jones, A. Thomas, R. S. Evans, S. J. Welch, P. J. Haug & G. L. Snow, ‘‘Forecasting daily patient volumes in the emergency department’’, Academic Emergency Medicine 15 (2008) 159. https://doi.org/10.1111/j. 1553-2712.2007.00032.x.

D. Tandberg & F. C. Quails, ‘‘Time Series Forecasts of Emergency Department Patient Volume, Length of Stay, and Acuity’’, Annals of Emergency Medicine 23 (1994) 299. https://doi.org/10.1016/S0196-0644(94)70044-3.

L. M. Schweigler, J. S. Desmond, M. L. McCarthy, K. J. Bukowski, E. L. Ionides & J. G. Younger, ‘‘Forecasting models of emergency department crowding’’, Academic Emergency Medicine 16 (2009) 301. https://doi.org/ 10.1111/j.1553-2712.2009.00356.x.

N. K. Rathlev, J. Chessare, J. Olshaker, D. Obendorfer, S. D. Mehta, T. Rothenhaus, S. Crespo, B. Magauran, K. Davidson, R. Shemin & K. Lewis, ‘‘Time Series Analysis of Variables Associated With Daily Mean Emergency Department Length of Stay’’, Annals of Emergency Medicine 49 (2007) 265. https://doi.org/10.1016/j.annemergmed.2006.11.007.

F. Kadri, F. Harrou, S. Chaabane & C. Tahon, ‘‘Time series modelling and forecasting of emergency department overcrowding’’, J. Med. Syst. 38 (2014) 1. https://doi.org/10.1007/s10916-014-0107-0.

Y. Sun, B. H. Heng, Y. T. Seow & E. Seow, ‘‘Forecasting daily attendances at an emergency department to aid resource planning’’, BMC Emerg. Med. 9 (2009) 1. https://doi.org/10.1186/1471-227X-9-1.

Y. Li, F. Wu, C. Zheng, K. Hou, K. Wang, N. Sun, B. Xu, J. Zhao & Y Li, ‘‘Predictive Analysis of Outpatient Volumes of a First-class Grade A General Hospital through ARIMA Models’’, Chinese Medical Record English Edition 2 (2014) 364. https://doi.org/10.3109/23256176.2014.992172.

M. Obubu, O. A. Oyafajo, A. I. Fidelia & O. J. Ibidoja, ‘‘Modeling Typhoid Mortality with Box-Jenkins Autoregressive Integrated Moving Average Models’’, Scholars Journal of Physics, Mathematics and Statistics 6 (2019) 29. https://doi.org/10.21276/sjpms.2019.6.3.2.

A. S. Oladimeji & O. J. Ibidoja, ‘‘The Distribution of Service Time of Patients’’, Journal of Reliability and Statistical Studies 13 (2020) 61. https: //doi.org/10.13052/jrss0974-8024.1313.

U. M. Aliyu, K. B. Gamagiwa, O. J. Ibidoja & M. Garba, ‘‘Application of Queuing Theory in a University Clinic’’, International Journal of Science for Global Sustainability 8 (2022) 9. https://doi.org/10.57233/ijsgs. v8i1.338.

G. S. Dheri, S. Pal, V. Singh, S. Marwaha & O. P. Choudhary, Hands-on Training on ‘‘Statistical Tools and Database Management In Agriculture", Reference Manual of training programme under ICAR NAHEP-CAAST-SNRM organized in collaboration with ICAR-IASRI (under NAHEP Component 2), Punjab Agricultural University, Ludhiana Publiation, 2019 pp. 95–100. https://nahep.icar.gov. in/API/Content/Uploads/84463b2f-f3e3-4baf-bb64-eae3d2496019/ 847ae7ac-d669-46e4-94a1-e7d31e5190a4.pdf.

D. Alexander, R. Fried & T. Liboschik, ‘‘Robust estimation of (partial) autocorrelation’’, Wiley Interdiscip Rev Comput Stat 7 (2015) 205. https: //doi.org/10.1002/wics.1351

O.A. Emmanuel& O.J. Ibidoja, ‘‘Autoregressive Modelfor CocoaProduction in Nigeria’’, International Journal of Science for Global Sustainability 2 (2016) 65. https://www.fugus-ijsgs.com.ng/index.php/ijsgs/article/view/ 216.

P. R. Hansen & A. Lunde, ‘‘Estimating the Persistence and the Autocorrelation Function of a Time Series that is Measured with Error’’, Econ Theory 30 (2014) 60. https://doi.org/10.1017/S0266466613000121.

A. Rogachev & E. Melikhova, ‘‘Creating a neural network system for forecasting and managing agricultural production using autocorrelation functions of time series’’, E3S Web of Conferences 164 (2020) 06005. https: //doi.org/10.1051/e3sconf/202016406005.

J. Mohamed, ‘‘Time Series Modeling and Forecasting of Somaliland Consumer Price Index: A Comparison of ARIMA and Regression with ARIMA Errors’’, American Journal of Theoretical and Applied Statistics 9 (2020) 143. https://doi.org/10.11648/j.ajtas.20200904.18.

S. Noureen, S. Atique, V. Roy & S. Bayne, Analysis and application of seasonal ARIMA model in Energy Demand Forecasting: A case study of small scale agricultural loan, IEEE 62nd International Midwest Symposium on Circuits and Systems (MWSCAS), Dallas, TX, USA, 2019, pp. 521-524. https://doi.org/10.1109/MWSCAS.2019.8885349.

E. Beard, J. Marsden, J. Brown, I. Tombor, J. Stapleton, S. Michie & R. West, ‘‘Understanding and using time series analyses in addiction research’’, Addiction 114 (2019) 1866. https://doi.org/10.1111/add.14643.

E. P. Clement, ‘‘Using Normalized Bayesian Information Criterion (Bic) to Improve Box-Jenkins Model Building’’, American Journal of Mathematics and Statistics 4 (2014) 214. https://doi.org/10.5923/j.ajms.20140405.02.

O.J.Ibidoja, F.P.Shan, J.Sulaiman&M.K.M.Ali, ‘‘RobustM-Estimators and Machine Learning Algorithms for Improving the Predictive Accuracy of Seaweed Contaminated Big Data’’, Journal of the Nigerian Society of

Physical Sciences 5 (2023) 1137. https://doi.org/10.46481/jnsps.2023.1137

A. D. W. Sumari, D. S. Charlinawati & Y. Ariyanto, ‘‘A Simple Approach using Statistical-based Machine Learning to Predict the Weapon System Operational Readiness’’, The 1st International Conference on Data Science and Official Statistics 2021 (2021) 343. https://doi.org/10.34123/icdsos. v2021i1.58.

Published

2023-08-20

How to Cite

Modelling Patients Waiting and Service Time by ARIMA Model: A Case of Federal University Gusau Clinic. (2023). Recent Advances in Natural Sciences, 1(1), 7. https://doi.org/10.61298/rans.2023.1.1.7

Issue

Volume 1, Issue 1, June 2023

Section

Articles
Copyright & Licensing

Copyright (c) 2023 Aliyu Usman Moyi, Kabir Bello, Olayemi Joshua Ibidoja, Garba Muhammad

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Modelling Patients Waiting and Service Time by ARIMA Model: A Case of Federal University Gusau Clinic. (2023). Recent Advances in Natural Sciences, 1(1), 7. https://doi.org/10.61298/rans.2023.1.1.7