The Average Run Length of the Cumulative Sum Chart When a <i>V</i>-Mask is Used

Kemp, Kenneth W.

doi:10.1111/j.2517-6161.1961.tb00398.x

Cited by 67 publications

(34 citation statements)

References 5 publications

(4 reference statements)

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“…In some cases, properties for the two-sided chart can be expressed in terms of corresponding properties for the simpler one-sided charts. Under the condition Ihu -&I 5 ku + kL, (3.6) it is well known that ANSSr = ANS&,ANSSJ(ANSS,, + ANSSJ (3.7) (Kemp 1961). The condition (3.6) ensures that 1 onesided chart will always begin cumulation from 0 on the next sample when the other one-sided chart signals.…”

Section: Properties Of Vsi Chartsmentioning

confidence: 96%

CUSUM Charts With Variable Sampling Intervals

Amin²,

1990

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A standard cumulative sum (CUSUM) chart for controlling the process mean takes samples from the process at fixed-length sampling intervals and uses a control statistic based on a cumulative sum of differences between the sample means and the target value. This article proposes a modification of the standard CUSUM scheme that varies the time intervals between samples depending on the value of the CUSUM control statistic. The variable sampling interval (VSI) CUSUM chart uses short sampling intervals if there is an indication that the process mean may have shifted and long sampling intervals if there is no indication of a change in the mean. If the CUSUM statistic actually enters the signal region, then the VSI CUSUM chart signals in the same manner as the standard CUSUM chart. A Markov-chain approach is used to evaluate properties such as the average time to signal and the average number of samples to signal. Results show that the proposed VSI CUSUM chart is considerably more efficient than the standard CUSUM chart. Tables are provided to aid in the design of VSI CUSUM charts.

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Section: Properties Of Vsi Chartsmentioning

confidence: 96%

CUSUM Charts With Variable Sampling Intervals

Amin²,

1990

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“…The simplest relation is obtained when upper and lower schemes do not interact-that is, if every realization of the process of observations has the property that, at the point where the upper scheme signals, the lower scheme is necessarily 0 and vice versa. Under the preceding assumptions, one obtains the ARL of the two-sided scheme in terms of its one-sided counterparts by using the classic formula due to Kemp (1961 If the noninteraction condition is satisfied, the preceding relation for the ARL remains valid for processes with serial correlation, provided that the RL is interpreted in the following way: Both upper and lower schemes are set to 0 after a signal produced by the process {Xi} that has reached a steady state, and the RL represents the number of observations taken from this moment until an out-of-control signal is produced. To see why this is true, let us perform the following experiment based on a single realization of the process {X,>, starting from the steady state: (a) Run upper and lower schemes in parallel.…”

Section: Discussionmentioning

confidence: 99%

Performance of CUSUM Control Schemes for Serially Correlated Observations

Yashchin

1993

Technometrics

101

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This article discusses situations in which one is interested in evaluating the run-length characteristics of a cumulative sum control scheme when the underlying data show the presence of serial correlation. In practical applications, situations of this type are common in problems associated with monitoring such characteristics of data as forecasting errors, measures of model adequacy, and variance components. The discussed problem is also relevant in situations in which data transformations are used to reduce the magnitude of serial correlation. The basic idea of analysis involves replacing the sequence of serially correlated observations by a sequence of independent and identically distributed observations for which the runlength characteristics of interest are roughly the same. Applications of the proposed method for several classes of processes arising in the area of statistical process control are discussed in detail, and it is shown that it leads to approximations that can be considered acceptable in many practical situations.

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“…The number ARL corresponds to the two-sided cusum test. It can be proven that the average run length (ARL) of a two-sided test is given by (Kemp, 1961;Van Dobben de Bruyn, 1968): (17) For example, if we select an ARL* -500 and ARL = 500, then the ARL for the combined scheme is ARL = 250. That means that if an upward and a downward cusum are maintained simultaneously, then the ARL until the first of them triggers a signal is one half of the 500 (= 250).…”

Section: The Choice Ol the Parameters H And Kmentioning

confidence: 99%

Automatic and Online Detection of Small but Persistent Shifts in GPS Station Coordinates by Statistical Process Control

Mertikas

2001

GPS Solutions

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This paper describes algorithms to detect sudden and persistent changes of small magnitude in the GPS baseline solution vectors or station coordinates. The aim of the algorithms is to monitor and control the quality of GPS measurements for critical real-time and crustal deformation applications using statistical process control. Quality control is a major problem in GPS, especially where realtime, automatic, and reliable positioning is needed, such as in the case of the GPS crustal deformation-monitoring network (GEONET) of Japan.To monitor the quality of baseline solutions the statistical techniques ofShewhart and cumulative sum charts are implemented.

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The Average Run Length of the Cumulative Sum Chart When a V-Mask is Used

Cited by 67 publications

References 5 publications

CUSUM Charts With Variable Sampling Intervals

CUSUM Charts With Variable Sampling Intervals

Performance of CUSUM Control Schemes for Serially Correlated Observations

Automatic and Online Detection of Small but Persistent Shifts in GPS Station Coordinates by Statistical Process Control

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