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The computation of average run length and average time to signal: an overview
Journal of Statistical Computation and Simulation, 2013Control charts are widely used in industries to monitor a process for quality improvement. Evaluation of the average run length (ARL) or average time to signal (ATS) plays an important role in the design of control charts and performance comparison. In this paper, we review several basic and popular procedures, including the Markov chain and integral ...
Zhonghua Li +3 more
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Average Run Lengths in Cumulative Chart Quality Control Schemes
Technometrics, 1961Average run-lengths are evaluated for V-mask quality control schemes based on cumulative deviation charts when the observations are Normally distributed and either independent or members of a certain serially correlated class.
P. L. Goldsmith, H. Whitfield
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International Journal of Production Research, 2016
This paper examines the exponentially weighted moving average (EWMA) chart with estimated process parameters. As the run length distribution is skewed when the process is in-control or slightly out-of-control, the average run length (ARL) provides less meaningful interpretation of a chart’s performance.
You, H.W. +3 more
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This paper examines the exponentially weighted moving average (EWMA) chart with estimated process parameters. As the run length distribution is skewed when the process is in-control or slightly out-of-control, the average run length (ARL) provides less meaningful interpretation of a chart’s performance.
You, H.W. +3 more
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Exact Average Run Lengths for Monitoring Poisson Counts
Communications in Statistics - Theory and Methods, 2014Control charts are widely employed in public health surveillance. One use is as an aid in monitoring rare health events. A chart is designed to exhibit acceptable average run lengths both when the process is in and out of control. Thus, the chart provides a real-time assessment of the situation.
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Computational Statistics & Data Analysis, 1999
Cuscore charts have recently been proposed as a statistical process monitoring tool designed to cope with situations in which special kinds of signals are feared a priori because they are known to affect the particular system being monitored. This paper provides algorithms to compute average run lengths and corresponding run length probability ...
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Cuscore charts have recently been proposed as a statistical process monitoring tool designed to cope with situations in which special kinds of signals are feared a priori because they are known to affect the particular system being monitored. This paper provides algorithms to compute average run lengths and corresponding run length probability ...
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Average run lengths for cusum control charts applied to residuals
Communications in Statistics - Theory and Methods, 1995A common approach to building control charts for autocorrelated data is to apply classical SPC to the residuals from a time series model of the process. However, Shewhart charts and even CUSUM charts are less sensitive to small shifts in the process mean when applied to residuals than when applied to independent data.
George C. Runger +2 more
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Study of average run lengths for supplementary runs rules in the presence of autocorrelation
Communications in Statistics - Simulation and Computation, 1994The basic assumption underlying statistical control chart criteria is that the process measurements are independent and identically distributed over time. However, autocorrelation and other time-series effects occur frequently in application. In this paper, the effects of autocorrelation are investigated for the frequently advocated supplementary runs ...
Alwan, Layth C. +2 more
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EXPLICIT FORMULA OF AVERAGE RUN LENGTH OF MOVING AVERAGE CONTROL CHART FOR POISSON INMA(1) PROCESS
Advances and Applications in Statistics, 2018Summary: Average run length (ARL) is widely used for measuring the performance of a control chart. In this work, the objective is to prove the ARL explicit formulas of the moving average control chart (MA chart) for the Poisson integer-valued moving average of order 1 (PoiINMA(1)). By comparing the accuracy of the ARL explicit formulas with that of the
Sukparungsee, Saowanit +2 more
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Algorithm AS 258: Average Run Lengths for Cumulative Sum Schemes
Applied Statistics, 1990CUSUM schemes are most commonly characterized by the average run length (ARL). The algorithms described here calculate ARLs for one- or two-sided CUSUM schemes.
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