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X-bar chart

About: X-bar chart is a research topic. Over the lifetime, 1049 publications have been published within this topic receiving 28427 citations.


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Journal ArticleDOI
S. W. Roberts1
TL;DR: In this article, a graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r, and all previous observations weights decreasing in geometric progression from the most recently back to the first.
Abstract: A geometrical moving average gives the most recent observation the greatest weight, and all previous observations weights decreasing in geometric progression from the most recent back to the first. A graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r. The properties of control chart tests based on geometric moving averages are compared to tests based on ordinary moving averages.

1,490 citations

Journal ArticleDOI
TL;DR: The purpose of this paper is to exposit a control chart technique that may be of value to both manufacturing and continuous process quality control engineers: the exponentially weighted moving average (EWMA) control chart.
Abstract: The Shewhart and CUSUM control chart techniques have found wide application in the manufacturing industries. However, workpiece quality has also been greatly enhanced by rapid and precise individual item measurements and by improvements in automatic dynamic machine control. One consequence is a growing similarity in the control problems faced by the workpiece quality control engineer and his compatriot in the continuous process industries. The purpose of this paper is to exposit a control chart technique that may be of value to both manufacturing and continuous process quality control engineers: the exponentially weighted moving average (EWMA) control chart. The EWMA has its origins in the early work of econometricians, and although its use in quality control has been recognized, it remains a largely neglected tool. The EWMA chart is easy to plot, easy to interpret, and its control limits are easy to obtain. Further, the EWMA leads naturally to an empirical dynamic control equation.

856 citations

Journal ArticleDOI
TL;DR: In this article, the authors unify and extend previously published characterizations of moving average, geometric moving average and cumulative sum control chart procedures, and present comparable characterisations of two procedures based on tests described but not evaluated in earlier papers.
Abstract: This paper unifies and extends previously published characterizations of moving average, geometric moving average, and cumulative sum control chart procedures. It presents comparable characterizations of two procedures based on tests described but not evaluated in earlier papers. One of these procedures is based on a test devised by Girshick and Rubin that is optimal under a particular set of idealized conditions. The other procedure is based on run sum tests, which are generalizations of the type of run test that counts the number of consecutive points that exceed a limit, the generalization taking into account the extent that points in such a run exceed the limit.

534 citations

Journal ArticleDOI
TL;DR: The variable sampling interval (VSI) chart as discussed by the authors uses a short sampling interval if the sample is close to but not actually outside the control limits, and a long sampling interval for the sample if it is closer to target.
Abstract: The usual practice in using a control chart to monitor a process is to take samples from the process with fixed sampling intervals. This article considers the properties of the chart when the sampling interval between each pair of samples is not fixed but rather depends on what is observed in the first sample. The idea is that the time interval until the next sample should be short if a sample shows some indication of a change in the process and long if there is no indication of a change. The proposed variable sampling interval (VSI) chart uses a short sampling interval if is close to but not actually outside the control limits and a long sampling interval if is close to target. If is actually outside the control limits, then the chart signals in the same way as the standard fixed sampling interval (FSI) chart. Properties such as the average time to signal and the average number of samples to signal are evaluated. Comparisons between the FSI and the VSI charts indicate that the VSI chart is substantially ...

473 citations

Journal ArticleDOI
TL;DR: The problem of detecting a shift of a percentile of a Weibull population in a process monitoring situation is considered and the proposed bootstrap percentile charts indicate a shift in the process percentile substantially quicker than the previously existing chart, while maintaining comparable average run lengths when the process is in control.
Abstract: The problem of detecting a shift of a percentile of a Weibull population in a process monitoring situation is considered. The parametric bootstrap method is used to establish lower and upper control limits for monitoring percentiles when process measurements have a Weibull distribution. Small percentiles are of importance when observing tensile strength and it is desirable to detect their downward shift. The performance of the proposed bootstrap percentile charts is considered based on computer simulations, and some comparisons are made with an existing Weibull percentile chart. The new bootstrap chart indicates a shift in the process percentile substantially quicker than the previously existing chart, while maintaining comparable average run lengths when the process is in control. An illustrative example concerning the tensile strength of carbon fibers is presented. Copyright © 2005 John Wiley & Sons, Ltd.

413 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202333
202271
20191
201817
201779
201664