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Quality in Production—Process Control I
Published in K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur, A First Course in Quality Engineering, 2018
K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur
A few more sophisticated control charts are available in the literature that are useful under some special circumstances. The cumulative sum chart is used when higher sensitivity is needed to discover small changes. The exponentially weighted moving average (EWMA) chart is also useful when small changes must be detected. In addition, the EWMA chart and the moving average chart are preferred when multiple units are not available in quick succession and, therefore, X¯- and R-charts cannot be used. The median chart is known to perform well with populations that are not normally distributed. Details of these charts can be found in textbooks in statistical quality control such as Montgomery (2013) and Grant and Leavenworth (1996).
General introduction
Published in Adedeji B. Badiru, Handbook of Industrial and Systems Engineering, 2013
where et=Xt-Xˆt,λ1=kP+kI+kD,λ2=-kP+-kD, and λ3=kD. The PID-based charts monitor et and include the SCC, EWMA, and M-M charts as special cases. Jiang et al. (2002) shows that the predictors of the EWMA chart and M-M chart may sometimes be inefficient and the SCC may be too sensitive to model deviation. On the other hand, the performance of the PID-based chart can be predicted via chart parameters through measures of two "capability indices." As a result, for any given underlying process, one can tune the parameters of the PID-based chart to optimize its performance.
Cumulative Sum (CUSUM) Chart
Published in William A. Levinson, Short-Run SPC for Manufacturing and Quality Professionals, 2023
The exponentially weighted moving average (EWMA) chart also is useful for detecting relatively small discrepancies between the process mean and the nominal, and is easier to use. This chapter will address EWMA in detail later.
Run length properties of run rules EWMA chart using integral equations
Published in Quality Technology & Quantitative Management, 2019
Petros E. Maravelakis, Philippe Castagliola, Michael B. C. Khoo
The EWMA chart is a popular tool for process monitoring. It is a control chart with memory and it is able to detect small to moderate shifts quickly. A technique that can improve the EWMA chart’s ability to signal is to use it in conjunction with runs rules. In this paper, we studied the run length properties of the 2 / 2 EWMA chart. This chart signals when two consecutive points are plotted either below a lower signalling limit or above an upper signalling limit. We derived suitable integral equations that can be used to exactly compute the probability mass function of the run length along with its first two non-central moments. The integral equations approach is an exact method in comparison to the simulation and the Markov chain methodology that are only approximations. Moreover, the Markov chain methodology results in very large transition probability matrices that makes the computational part unwieldy. Note that the methodology used for the 2 / 2 EWMA chart can be used for the general class of these control charts, that is the r / s EWMA chart. Finally, with a suitable modification, the methodology proposed in this paper can be used for calculating the probability mass function of the run length, as well as the ARL and the SDRL of a self-starting run rules control chart.
Enhanced operation of wastewater treatment plant using state estimation-based fault detection strategies
Published in International Journal of Control, 2021
Imen Baklouti, Majdi Mansouri, Ahmed Ben Hamida, Hazem Numan Nounou, Mohamed Nounou
EWMA chart is applied to monitor variables in statistical control process which is different from other control charts, tents to consider each data point individually (Corominas et al., 2011; Patel & Divecha, 2011). In the literature, (Baklouti, Mansouri, Hamida, Nounou, & Nounou, 2018a, 2018b) the EWMA (Roberts, 1959) has received a great deal of attention in terms of robustness and efficiency to perform well for small shifts compared to the other especially univariate techniques.
The case against generally weighted moving average (GWMA) control charts
Published in Quality Engineering, 2022
Sven Knoth, William H. Woodall, Víctor G. Tercero-Gómez
As the name indicates, the GWMA chart is based on statistics which are weighted averages of the observations collected over time. It is a generalization of the exponentially weighted moving average (EWMA) chart for which the weights decrease exponentially with the age of the observations.