Exponential CUSUM Charts with Estimated Control Limits

Zhang, Min; Megahed, Fadel M.; Woodall, William H.

doi:10.1002/qre.1495

Cited by 107 publications

(101 citation statements)

References 19 publications

(44 reference statements)

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“…For this reason, TBE control charts are often called exponential control charts. Since Lucas (1985) and Vardeman and Ray (1985) first proposed the TBE control chart, many recent studies have focused on the TBE control chart, including the exponential chart (Chan, Xie, and Goh 2000;Chan et al 2002;Jones and Champ 2002;Xie, Goh, and Ranjan 2002;Zhang, Xie, and Goh 2005;Zhang, Xie, and Goh 2006;Zhang et al 2011;Dovoedo and Chakraborti 2012), the exponential CUSUM chart (Lucas 1985;Gan 1994;Borror, Kates, and Montgomery 2003;Cheng and Chen 2011;Qu et al 2013;Zhang, Megahed, and Woodall 2014) and the exponential EWMA chart (Gan 1998;Ozsan, Testik, and Wei 2010;Chen 2012).…”

Section: Introductionmentioning

confidence: 99%

Design of exponential control charts based on average time to signal using a sequential sampling scheme

Yang

Cheng

et al. 2015

International Journal of Production Research

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2015) Design of exponential control charts based on average time to signal using a sequential sampling schemeExponential charts based on time-between-events (TBE) data are widely investigated and applied in various fields. The average time to signal (ATS) is used instead of the average run length to evaluate the performance of TBE charts, since the ATS involves both the number and the time of samples inspected until a signal occurs. An ATS-unbiased exponential control chart is proposed when the in-control parameter is known. Considering the need in practice to start monitoring a production process as soon as possible, a sequential sampling scheme is adopted and the in-control parameter is estimated by an unbiased and consistent estimator. Some specific guidelines to stop updating control limits are obtained from the relationship between the phase I sample size and the actual false alarm rate. Finally, two real examples are given to illustrate the implementation and efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Design of exponential control charts based on average time to signal using a sequential sampling scheme

Yang

Cheng

et al. 2015

International Journal of Production Research

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“…It is well‐known that better performance is achieved when the AARL value is close to the desired ARL value with an acceptable small SDARL value. In most of the previous studies, the researchers considered an SDARL value within 10% of the desired in‐control ARL value to be satisfactory; see Zhang et al The SDARL metric can be calculated as follows

italicSDARL = \sqrt{E ((), A R L^{2}) - {[E (A R L)]}^{2}} .

…”

Section: Performance Evaluationmentioning

confidence: 99%

An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

Hany

Mahmoud

2015

Qual. Reliab. Engng. Int.

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We evaluate the performance of the Crosier's cumulative sum (C‐CUSUM) control chart when the probability distribution parameters of the underlying quality characteristic are estimated from Phase I data. Because the average run length (ARL) under estimated parameters is a random variable, we study the estimation effect on the chart performance in terms of the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL). Previous evaluations of this control chart were conducted while assuming known process parameters. Using the Markov chain and simulation approaches, we evaluate the in‐control performance of the chart and provide some quantiles for its in‐control ARL distribution under estimated parameters. We also compare the performance of the C‐CUSUM chart to that of the ordinary CUSUM (O‐CUSUM) chart when the process parameters are unknown. Our results show that large number of Phase I samples are required to achieve a quite reasonable performance. Additionally, the performance of the C‐CUSUM chart is found to be superior to that of the O‐CUSUM chart. Finally, we recommend the use of a recently proposed bootstrap procedure in designing the C‐CUSUM chart to guarantee, at a certain probability, that the in‐control ARL will be of at least the desired value using the available amount of Phase I data. Copyright © 2015 John Wiley & Sons, Ltd.

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“…They used it to study the effect of parameter estimation on the performance of the risk‐adjusted CUSUM chart. Zhang et al . studied the performance of the geometric and exponential CUSUM charts, respectively, using the SDARL metric.…”

Section: Introductionmentioning

confidence: 99%

The Performance of the Multivariate Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

Aly

Mahmoud

Hamed

2015

Quality & Reliability Eng

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The multivariate adaptive exponentially weighted moving average control chart (MAEWMA) can detect shifts of different sizes while diminishing the inertia problem to a large extent. Although it has several advantages compared to various multivariate charts, previous literature has not considered its performance when the parameters are estimated. In this study, the performance of the MAEWMA chart with estimated parameters is studied while considering the practitioner-topractitioner variation. This kind of variation occurs due to using different Phase I samples by different practitioners in estimating the unknown parameters. The simulation results in this paper show that estimating the parameters results in extensively excessive false alarms and as a result a large number of Phase I samples is needed to achieve the desired incontrol performance. Using small number of Phase I samples in estimating the parameters may result in an in-control ARL distribution that almost completely lies below the desired value. To handle this problem, we strongly recommend the use of a bootstrap-based algorithm to adjust the control limit of the MAEWMA chart. This algorithm enables practitioners to achieve, with a certain probability, an in-control ARL that is greater than or equal to the desired value while using the available number of Phase I samples.

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Exponential CUSUM Charts with Estimated Control Limits

Cited by 107 publications

References 19 publications

Design of exponential control charts based on average time to signal using a sequential sampling scheme

Design of exponential control charts based on average time to signal using a sequential sampling scheme

An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

The Performance of the Multivariate Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

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