INTEGRATION OF SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE AND BAYESIAN METHODS TO PREDICT PRODUCTION THROUGHPUT UNDER RANDOM VARIABLES
DOI:
https://doi.org/10.15282/jmes.7.2014.23.0121Keywords:
Production throughput; breakdown; demand; lead time; scrap.Abstract
Analysing and modelling efforts on production throughput are getting more complex due to random variables in today’s dynamic production systems. The objective of this study is to take multiple random variables of production into account when aiming for production throughput with higher accuracy of prediction. In the dynamic manufacturing environment, production lines have to cope with changes in set-up time, machinery breakdown, lead time of manufacturing, demand, and scrap. This study applied a Bayesian method to tackle the problem. Later, the prediction of production throughput under random variables is improved by the Seasonal Autoregressive Integrated Moving Average (SARIMA) method. The integrated Bayesian-SARIMA model consists of multiple random parameters with multiple random variables. A statistical index, R-squared, is used to measure the performance of the integrated model. A real case study on tile and ceramic production is considered. The Bayesian model is validated with respect to the convergence and efficiency of its outputs. The results of the analyses indicate that the Bayesian-SARIMA method produces a higher R-squared value, at 98.8%, compared with previous studies on Bayesian methods where the value was 90.68% and the ARIMA method where it was 97.38%. Consequently a robust approach in terms of the degree of prediction accuracy is proposed. This integrated method may be applied for the estimation of other production performance factors like lead time and cycle time in different types of dynamic manufacturing environment.
References
Alden J. Estimating performance of two workstations in series with downtime and unequal speeds. General Motors Research & Development Center, Report R&D-9434, Warren, MI. 2002.
Baker KR, Powell SG. A predictive model for the throughput of simple assembly systems. European Journal of Operational Research. 1995;81:336-45.
`Blumenfeld DE, Li J. An analytical formula for throughput of a production line with identical stations and random failures. Mathematical Problems in Engineering. 2005;2005:293-308.
Brooks SP, Gelman A. Alternative methods for monitoring convergence of iterative simulations. 1998.
Bolstad WM. Introduction to Bayesian statistics. New Jersey: John Wiley & Sons; 2004.
Dantzig GB. Planning under uncertainty. Annals of Operations Research. 1999;85:0-.
Tan HB. Business and economic forecasting: techniques and applications. Serdang, Selangor Darul Ehsan: Penerbit Universiti Putra Malaysia; 2006.
Congdon P. Bayesian Statistical Modelling. 2 ed. England: John Wiley & Sons; 2007.
Deif AM, ElMaraghy HA. Modelling and analysis of dynamic capacity complexity in multi-stage production. Production Planning & Control. 2009;20:737-49.
Gilks WR, Richardson S, Spiegelhalter D. Markov Chain Monte Carlo in practice. New York: Taylor & Francis; 1995.
Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis. Third Edition. Florida: Taylor & Francis; 2013.
Hoque Z. A contingency model of the association between strategy, environmental uncertainty and performance measurement: impact on organizational performance. International Business Review. 2004;13:485-502.
Koop G, Steel MF, Osiewalski J. Posterior analysis of stochastic frontier models using Gibbs sampling. Computational Statistics. 1992;10:353-73.
Koh SCL, Gunasekaran A. A knowledge management approach for managing uncertainty in manufacturing. Industrial Management & Data Systems. 2006;106:439-59.
Li L, Chang Q, Xiao G, Ambani S. Throughput bottleneck prediction of manufacturing systems using time series analysis. Journal of Manufacturing Science and Engineering. 2011;133:021015-.
Li J, Blumenfeld DE, Alden JM. Comparisons of two-machine line models in throughput analysis. International Journal of Production Research. 2006;44:1375-98.
Markel T, Brooker A, Hendricks T, Johnson V, Kelly K, Kramer B, et al. ADVISOR: a systems analysis tool for advanced vehicle modeling. Journal of Power Sources. 2002;110:255-66.
Li J, E. Blumenfeld D, Huang N, M. Alden J. Throughput analysis of production systems: recent advances and future topics. International Journal of Production Research. 2009;47:3823-51.
Mula J, Poler R, García-Sabater JP, Lario FC. Models for production planning under uncertainty: A review. International Journal of Production Economics. 2006;103:271-85.
Roberts GO. Markov chain concepts related to sampling algorithms. Markov chain Monte Carlo in practice: Springer; 1996. p. 45-57.
Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian approaches to clinical trials and health-care evaluation. New York: John Wiley; 2004.
Spiegelhalter D, Thomas A, Best N, Gilks W. BUGS 0.5: Bayesian inference using Gibbs sampling manual (version ii). MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK. 1996.
Sheu C-f, O’Curry S. Simulation-based bayesian inference using BUGS. Behavior Research Methods, Instruments, & Computers. 1998;30:232-7.
Zimmermann HJ. Intelligent manufacturing management. In: Kahraman C, editor. Fuzzy Applications in Industrial Engineering: Springer Berlin Heidelberg; 2006. p. 383-400.
