664 research outputs found
EWMA Chart and Measurement Error
Measurement error is a usually met distortion factor in real-world applications that influences the outcome of a process. In this paper, we examine the effect of measurement error on the ability of the EWMA control chart to detect out-of-control situations. The model used is the one involving linear covariates. We investigate the ability of the EWMA chart in the case of a shift in mean. The effect of taking multiple measurements on each sampled unit and the case of linearly increasing variance are also examined. We prove that, in the case of measurement error, the performance of the chart regarding the mean is significantly affected.Exponentially weighted moving average control chart, Average run length, Average time to signal, Measurement error, Markov chain, Statistical process control
ARL Evaluation of a DEWMA Control Chart for Autocorrelated Data: A Case Study on Prices of Major Industrial Commodities
The double exponentially weighted moving average (DEWMA) control chart, an extension of the EWMA control chart, is a useful statistical process control tool for detecting small shift sizes in the mean of processes with either independent or autocorrelated observations. In this study, we derived explicit formulas to compute the average run length (ARL) for a moving average of order q (MA(q)) process with exponential white noise running on a DEWMA control chart and verified their accuracy by comparison with the numerical integral equation (NIE) method. The results for both were in good agreement with the actual ARL. To investigate the efficiency of the proposed procedure on the DEWMA control chart, a performance comparison between it and the standard and modified EWMA control charts was also conducted to determine which provided the smallest out-of-control ARL value for several scenarios involving MA(q) processes. It was found that the DEWMA control chart provided the lowest out-of-control ARL for all cases of varying the exponential smoothing parameter and shift size values. To illustrate the efficacy of the proposed methodology, the presented approach was applied to datasets of the prices of several major industrial commodities in Thailand. The findings show that the DEWMA procedure performed well in almost all of the scenarios tested. Doi: 10.28991/ESJ-2023-07-05-020 Full Text: PD
An Examination of the Robustness to Non Normality of the EWMA Control Charts for the Dispersion
The EWMA control chart is used to detect small shifts in a process. It has been shown that, for certain values of the smoothing parameter, the EWMA chart for the mean is robust to non normality. In this article, we examine the case of non normality in the EWMA charts for the dispersion. It is shown that we can have an EWMA chart for dispersion robust to non normality when non normality is not extreme.Average run length, Control charts, Exponntially weighted moving average control chart, Median run length, Non normality, Statistical process control
The Multivariate EWMA Model and Health Care Monitoring
We introduce the construction of MEWMA (Multivariate exponentially weighted movingaverage) process control in the field of bio surveillance. Such introduction will both improve the reliability of data collected in bio surveillance, better interpretation of the results,improvement in the quality of results and standardization of results when more than two variables are involved. We propose sensitivity ratios as a measure of the effects of the mean shift and dispersion shift in processes under study. Using these sensitivity measures, we designed the optimal exponential weighting factor, which is consistent to results reported in control chart applications. Although ARL (average run length) is the usual measure for control chart performance in multivariate process control, it is by no means the only criterion, however, at the moment it is most widely used criterion for decision making. We suggest addition study of other criteria. For example Medial Run Length, Days to Completion, Direction of Eorrors and others
Improving Sensitivity of the DEWMA Chart with Exact ARL Solution under the Trend AR(p) Model and Its Applications
The double exponentially weighted moving average (DEWMA) chart is a control chart that is a vital analytical tool for keeping track of the quality of a process, and the sensitivity of the control chart to the process is evaluated using the average run length (ARL). Herein, the aim of this study is to derive the explicit formula of the ARL on the DEWMA chart with the autoregressive with trend model and its residual, which is exponential white noise. This study shows that this proposed method was compared to the ARL derived using the numerical integral equation (NIE) approach, and the explicit ARL formula decreased the computing time. By changing exponential parameters that were relevant to evaluating in various circumstances, the sensitivity of AR(p) with the trend model with the DEWMA chart was investigated. These were compared with the EWMA and CUSUM charts in terms of the ARL, standard deviation run length (SDRL), and median run length (MRL). The results indicate that the DEWMA chart has the highest performance, and when it was small, the DEWMA chart had high sensitivity for detecting processes. Digital currencies are utilized to demonstrate the efficacy of the proposed method; the results are consistent with the simulated data. Doi: 10.28991/ESJ-2023-07-06-03 Full Text: PD
A Nonparametric HEWMA-p Control Chart for Variance in Monitoring Processes
Control charts are considered as powerful tools in detecting any shift in a process. Usually, the Shewhart control chart is used when data follows the symmetrical property of a normal distribution. In practice, the data from the industry may follow a non-symmetrical distribution or an unknown distribution. The average run length (ARL) is a significant measure to assess the performance of the control chart. The ARL may mislead when the statistic is computed from an asymmetric distribution. To handle this issue, in this paper, an ARL-unbiased hybrid exponentially weighted moving average proportion (HEWMA-p) chart is proposed for monitoring the process variance for a non-normal distribution or an unknown distribution. The efficiency of the proposed chart is compared with the existing chart in terms of ARLs. The proposed chart is more efficient than the existing chart in terms of ARLs. A real example is given for the illustration of the proposed chart in the industry.11Ysciescopu
Using the moving average and exponentially weighted moving average with COVID 19
The study was concerned with clarifying the work of the quality control charts and their application in the health field, where the quality control charts for the moving average and the Exponential Weighted moving average were used to clarify the number of people infected with the Corona virus (COVID 19) for the month of April of the year 2020 and compare it with the number of people infected with the virus for the month of April of 2021, where these charts were drawn and it was found The number of injured in April 2021 is more than in April 2020, and the drawings showed the upper and lower limits of the level of injury in addition to the average number of injuries . The graphics showed the number of days out of control in the animations of moving averages and Exponential Weighted moving averages, and the study showed citizens' lack of interest in preventive methods that reduce infection with this virus and their lack of interest in urban health and not taking the vaccine for this virus in a timely manner
A Binary Control Chart to Detect Small Jumps
The classic N p chart gives a signal if the number of successes in a sequence
of inde- pendent binary variables exceeds a control limit. Motivated by
engineering applications in industrial image processing and, to some extent,
financial statistics, we study a simple modification of this chart, which uses
only the most recent observations. Our aim is to construct a control chart for
detecting a shift of an unknown size, allowing for an unknown distribution of
the error terms. Simulation studies indicate that the proposed chart is su-
perior in terms of out-of-control average run length, when one is interest in
the detection of very small shifts. We provide a (functional) central limit
theorem under a change-point model with local alternatives which explains that
unexpected and interesting behavior. Since real observations are often not
independent, the question arises whether these re- sults still hold true for
the dependent case. Indeed, our asymptotic results work under the fairly
general condition that the observations form a martingale difference array.
This enlarges the applicability of our results considerably, firstly, to a
large class time series models, and, secondly, to locally dependent image data,
as we demonstrate by an example
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