Shingwenyana, MxengeniMalela-Majika, Jean-ClaudeCastagliola, PhilippeHuman, Schalk William2024-07-042024Mxengeni Shingwenyana, Jean-Claude Malela-Majika, Philippe Castagliola & Schalk W. Human (2024) A Bayesian ARMA-GARCH EWMA monitoring scheme for long run: A case study on monitoring the USD/ZAR exchange rate, Quality Engineering, 36:3, 471-486, DOI: 10.1080/08982112.2023.2234458.0898-2112 (print)1532-4222 (online)10.1080/08982112.2023.2234458http://hdl.handle.net/2263/96796Statistical process monitoring (SPM) offers an important toolkit used to monitor the stability of a process to improve the quality of outputs and/or services. More often, the design of control charts requires the estimation of the probability density function that involves selecting a common distribution that facilitates the estimation of the process parameters. The Bayesian approach is one of the most efficient techniques used in such instances. It incorporates informative and non-informative priors, i.e., uses information on past data and charting structures, to estimate parameters more efficiently than classical approaches. Bayesian approaches reduce the total expected cost over a finite horizon or the long-run expected average cost. This paper introduces a new Bayesian exponentially weighted moving average (EWMA) monitoring scheme for long runs based on an ARMA-GARCH model. The properties of the new monitoring scheme are investigated in terms of the run-length distribution. A case study on monitoring the USD to ZAR exchange rate is provided using the proposed Bayesian ARMA-GARCH EWMA monitoring scheme.en© 2023 Taylor & Francis Group, LLC. This is an electronic version of an article published in Quality Engineering, vol. 36, no. 3, pp. 471-486, 2024. doi : 10.1080/08982112.2023.2234458. Quality Engineering is available online at: https://www.tandfonline.com/loi/lqen20.Autoregressive moving average (ARMA)Generalized autoregressive conditional heteroskedasticity (GARCH)ARMA-GARCHBayesian approachControl chartExponentially weighted moving average (EWMA)Financial dataPrior distributionPosterior distributionStatistical process monitoring (SPM)SDG-08: Decent work and economic growthPostprint Article