Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL

Lee, Ming Ha; Khoo, Michael B. C.

doi:10.1080/03610910600716779

Cited by 29 publications

(20 citation statements)

References 34 publications

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“…For example, when δ =1 and p =3, we have ( r ∗ , H ∗ )=(0.1445,9.2157). When δ =1 and p =20, we have ( r ∗ , H ∗ )=(0.0998,35.6484). Our numerical results are consistent with those provided by Crowder for the optimal statistical design of the univariate EWMA chart and by Lee and Khoo for the optimal statistical design of the MEWMA chart.…”

Section: Performance Of the Mewma‐coda Control Chartsupporting

confidence: 88%

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Tran

Castagliola

Celano

et al. 2018

Quality & Reliability Eng

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Recently, the monitoring of compositional data by means of control charts has been investigated in the statistical process control literature. In this article, we develop a Phase II multivariate exponentially weighted moving average control chart, for the continuous surveillance of compositional data based on a transformation into coordinate representation. We use a Markov chain approximation to determine the performance of the proposed multivariate control chart. The optimal multivariate exponentially weighted moving average smoothing constants, control limits, and out‐of‐control average run lengths have been computed for different combinations of the in‐control average run lengths and the number of variables. Several tables are presented and enumerated to show the statistical performance of the proposed control chart. An example illustrates the use of this chart on an industrial problem from a plant in Europe.

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Section: Performance Of the Mewma‐coda Control Chartsupporting

confidence: 88%

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Tran

Castagliola

Celano

et al. 2018

Quality & Reliability Eng

Self Cite

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“…By providing optimal design procedures of the synthetic T 2 chart, based on MRL, for the zero-state and steady-state modes, this paper complements the work of Ghute and Shirke 2 , and Aparisi and de Luna 5 , who optimally designed the synthetic T 2 chart, based on only ARL, for the zero-state mode process. Note that in the literature, the optimal designs of MEWMA and MCUSUM charts based on ARL and MRL are already in existence (see for example, Lee and Khoo 22,25 ). Therefore, it is timely that the optimal designs of the synthetic T 2 chart based on MRL be made accessible to practitioners, so as to increase their confidence in using the said chart.…”

Section: Resultsmentioning

confidence: 98%

“…The MRL profiles and limits of the Hotelling's T 2 chart are calculated using the procedure presented in Khoo 23 but modified for the multivariate case, by means of a program written in Mathematica. In the computation of the transition probability matrices for the transient states, of the MEWMA chart, the procedure given in Lee and Khoo 22 is used, incorporating the one-dimensional Markov chain approach for the in-control process and the two-dimensional Markov chain approach for the out-of-control case. Note that for the case of the steady-state mode, the cyclical steady-state probability vector, s 0 (see Equation (9)), is used in place of the initial probability vector, s. The discretization for the one-dimensional Markov chain uses 60 states, whereas the discretization of the two-dimensional Markov chain uses m+1 states for the vertical axis and 2m+1 states for the horizontal axis, where m = 30.…”

Section: Performance Comparisonmentioning

confidence: 99%

Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length

Khoo

Wong

et al. 2011

Quality & Reliability Eng

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The average run length (ARL) is usually used as a sole measure of performance of a multivariate control chart. The Hotelling's T 2 , multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts are commonly optimally designed based on the ARL. Similar to the case of univariate quality control, in multivariate quality control, the shape of the run length distribution changes in accordance to the magnitude of the shift in the mean vector, from highly skewed when the process is in-control to nearly symmetric for large shifts. Because the shape of the run length distribution changes with the magnitude of the shift in the mean vector, the median run length (MRL) provides additional and more meaningful information about the in-control and out-of-control performances of multivariate charts, not given by the ARL. This paper provides a procedure for optimal designs of the multivariate synthetic T 2 chart for the process mean, based on MRL, for both the zero and steady-state modes. Two Mathematica programs, each for the zero state and steady-state modes are given for a quick computation of the optimal parameters of the synthetic T 2 chart, designed based on MRL. These optimal parameters are provided in the paper, for the bivariate case with sample sizes, n ∈{4, 7, 10}. The MRL performances of the synthetic T 2 , MEWMA and Hotelling's T 2 charts are also compared.

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“…Observe that, when p 0 = 0.50, this approach corresponds to the median run length criterion discussed by Gan (1993Gan ( , 1994 and Lee and Khoo (2006). A similar constraint on the GLR run-length distribution has also been proposed by Lai (2001) as a more tractable and more appropriate criterion than the ARL when the observations are not independent.…”

Section: Estimation Of the Control Limitmentioning

confidence: 99%

Practical Design of Generalized Likelihood Ratio Control Charts for Autocorrelated Data

Capizzi

Masarotto

2008

Technometrics

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Control charts based on Generalized Likelihood Ratio (GLR) tests are attractive from both a theoretical and practical point of view. In particular, in the case of an autocorrelated process, the GLR test uses the information contained in the time-varying response after a change and, as shown by Apley and Shi, is able to outperfom traditional control charts applied to residuals. In addition, a GLR chart provides estimates of the magnitude and the time of occurrence of the change. In this paper, we present a practical approach to the implementation of GLR charts for monitoring an autoregressive and moving average process assuming that only a Phase I sample is available. The proposed approach, based on automatic time series identification, estimates the GLR control limits via stochastic approximation using bootstrap resampling. Thus, it is able to take into account the uncertainty about the underlying model. A Monte Carlo study shows that our methodology can be used to design in a semi-automatic fashion a GLR chart with a prescribed rate of false alarms when as few as 50 Phase I observations are available. A real example is used to illustrate the designing procedure.

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Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL

Cited by 29 publications

References 34 publications

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length

Practical Design of Generalized Likelihood Ratio Control Charts for Autocorrelated Data

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