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Journal ArticleDOI

Cumulative Sum Charts

01 Feb 1961-Technometrics (Taylor & Francis Group)-Vol. 3, Iss: 1, pp 1-9
TL;DR: In this article, the development of process inspection schemes from the original methods of Shewhart to the new charts using cumulative sums, and surveys the present practice in the operation of schemes based on cumulative sums are presented.
Abstract: This paper, presented orally to the Gordon Research Conference on Statistics in Chemistry in July 1960, traces the development of process inspection schemes from the original methods of Shewhart to the new charts using cumulative sums, and surveys the present practice in the operation of schemes based on cumulative sums. In spitc of the completely different appearance of the visual records kept for Shewhart and cumulative sum charts, a continuous sequence of development from the one type of scheme to the other can be established. The criteria by which a particular process inspection scheme is chosen are also developed and the practical choice of schemes is described.
Citations
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Journal ArticleDOI
TL;DR: The data quality problem in the context of supply chain management (SCM) is introduced and methods for monitoring and controlling data quality are proposed and highlighted.

652 citations

Journal ArticleDOI
Stephen V. Crowder1
TL;DR: In this paper, a numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average (EWMA) charts, assuming normal observations, along with an example illustrating how to design such a chart.
Abstract: A numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average (EWMA) charts. Both average run lengths (ARL's) and standard deviations of run lengths (SDRL's) are presented for the twosided EWMA chart assuming normal observations, along with an example illustrating how to design such a chart. The procedure given extends easily to many nonnormal cases and to one-sided versions of the EWMA chart.

443 citations

Journal ArticleDOI
TL;DR: It is shown that data from consumer smartwatches can be used for the pre-symptomatic detection of coronavirus disease 2019 (COVID-19), and suggested that activity tracking and health monitoring via consumer wearable devices may beUsed for the large-scale, real-time detection of respiratory infections, often pre-Symptomatically.
Abstract: Consumer wearable devices that continuously measure vital signs have been used to monitor the onset of infectious disease. Here, we show that data from consumer smartwatches can be used for the pre-symptomatic detection of coronavirus disease 2019 (COVID-19). We analysed physiological and activity data from 32 individuals infected with COVID-19, identified from a cohort of nearly 5,300 participants, and found that 26 of them (81%) had alterations in their heart rate, number of daily steps or time asleep. Of the 25 cases of COVID-19 with detected physiological alterations for which we had symptom information, 22 were detected before (or at) symptom onset, with four cases detected at least nine days earlier. Using retrospective smartwatch data, we show that 63% of the COVID-19 cases could have been detected before symptom onset in real time via a two-tiered warning system based on the occurrence of extreme elevations in resting heart rate relative to the individual baseline. Our findings suggest that activity tracking and health monitoring via consumer wearable devices may be used for the large-scale, real-time detection of respiratory infections, often pre-symptomatically.

279 citations

Journal ArticleDOI
TL;DR: This work considers statistical process control when measurements are multivariate and proposes a cumulative sum (CUSUM) procedure, which is based on the cross-sectional antiranks of the measurements, which can detect shifts in all directions.
Abstract: We consider statistical process control when measurements are multivariate. A cumulative sum (CUSUM) procedure is suggested in detecting a shift in the mean vector of the measurements, which is based on the cross-sectional antiranks of the measurements. At each time point, the measurements are ordered and their antiranks, which are the indices of the order statistics, are recorded. When the process is in control and the joint distribution of the multivariate measurements satisfies some regularity conditions, the antirank vector at each time point has a given distribution. This distribution changes to some other distribution when the process is out of control and the components of the shift in the mean vector of the process are not all the same. This CUSUM can therefore detect shifts in all directions except the one in which the components of the shift in the mean vector are all the same but not 0. The shift with equal components, however, can be easily detected by another univariate CUSUM. The former CUSU...

181 citations

References
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Book
01 Jan 1931

2,588 citations

Journal ArticleDOI
TL;DR: A criterion that measures approximately the average net income of a process under surveillance of an X chart when the process is subject to random shifts in the process mean is established.
Abstract: This paper establishes a criterion that measures approximately the average net income of a process under surveillance of an X chart when the process is subject to random shifts in the process mean. The quality control rule assumed is that an assignable cause is looked for whenever a point falls outside the control limits. The criterion is for the case in which it is assumed that the process is not shut down while the search for the assignable cause is in progress, nor is the cost of adjustment or repair and the cost of bringing the process back into a state of control after the assignable cause is discovered charged to the control chart program. The paper shows how to determine the sample size, the interval between samples, and the control limits that will yield approximately maximum average net income. Numerical examples of optimum design are studied to see how variation in the various risk and cost factors affects the optimum. * The writer is greatly indebted to I. R. Savage and G. Greggory of ...

879 citations

Journal ArticleDOI
E. S. Page1

674 citations

Journal ArticleDOI

227 citations