EVVMA and cusum control charts in the presence of correlation

VanBrackle, Lewis; Reynolds, Marion R.

doi:10.1080/03610919708813421

Cited by 80 publications

(35 citation statements)

References 36 publications

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“…Because V t is a two-dimensional vector Markov process, two-dimensional Markov chain methods similar to those used by Runger and Prabhu (1996), VanBrackle andReynolds (1997), andJiang (2001) can be used to calculate the ARL of the control chart on y t . Readers familiar with automatic control theory might recognize (2) as the observable canonical form (Åström and Wittenmark 1990) of the filter.…”

Section: Average Run Length Calculation and Filter Optimization Strategymentioning

confidence: 99%

Optimal Design of Second-Order Linear Filters for Control Charting

Chin

Apley

2006

Technometrics

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In many common control charting situations, the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data. In recent work that has generalized this concept, the charted statistic is the output of a general linear filter in impulse response form, and the filter is designed by selecting its impulse response coefficients to optimize its average run length performance. In this work, we restrict attention to the class of all second-order linear filters applied to the residuals of a time series model of the process data. We present an algorithm for optimizing the design of the secondorder filter that is more computationally efficient and robust than the algorithm for optimizing the general linear filter. We demonstrate that the optimal second-order filter performs almost as well as the optimal general linear filter in many situations. Both methods share a number of interesting characteristics and are tuned to detect any distinct features of the process mean shift as it manifests itself in the residuals.

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Section: Average Run Length Calculation and Filter Optimization Strategymentioning

confidence: 99%

Optimal Design of Second-Order Linear Filters for Control Charting

Chin

Apley

2006

Technometrics

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“…When the primary goal is to detect changes of parameters associated with the marginal distribution such as mean or variance, the classical CUSUM procedure will be maintained and adjustments on the design will be made based on theoretical analysis or simulated results of operating characteristics. The effect of correlation on the operating characteristics is studied by Bagshaw and Johnson (1974), Yashchin (1993), Bohm and Hackl (1996), Vanbrackle and Reynolds (1997), Timmer et al (1999), Fuh (2003, and Busaba et al (2013). ν = max{n > 0 : T n = 0}, the last zero point of {T n } and the post-change parameter θ is estimated as the sample mean T N /(N −ν).…”

Section: Introductionmentioning

confidence: 98%

Inference for post-change parameters after sequential CUSUM test under AR(1) model

2016

Journal of Statistical Planning and Inference

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“…In literature, many different techniques have been proposed to eliminate the effect of autocorrelation in observations [4][5][6]. The primary technique is to fit an appropriate time series model to the observations and then apply traditional control charts such as Shewhart, Cumulative Sum Control Chart (CUSUM), and ExponentiallyWeighted Moving Average Chart (EWMA) to the residuals from this model [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Eliminating the influence of serial correlation on statistical process control charts using trend free pre-whitening (TFPW) method

Desa

Jemain²

2013

AIP Conference Proceedings

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A key assumption in traditional statistical process control (SPC) technique is based on the requirement that observations or time series data are normally and independently distributed. The presences of a serial autocorrelation results in a number of problems, including an increase in the type I error rate and thereby increase the expected number of false alarm in the process observation. However, the independency assumption is often violated in practice due to the influence of serial correlation in the observation. Therefore, the aim of this paper is to demonstrate with the hospital admission data, the influence of serial correlation on the statistical control charts. The trend free pre-whitening (TFPW) method has been used and applied as an alternative method to obtain residuals series which are statistically uncorrelated to each other. In this study, a data set of daily hospital admission for respiratory and cardiovascular diseases was used from the period of 1 January 2009 to 31 December 2009 (365 days). Result showed that TFPW method is an easy and useful method in removing the influence of serial correlation from the hospital admission data. It can be concluded that statistical control chart based on residual series perform better compared to original hospital admission series which influenced by the effects of serial correlation data.

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EVVMA and cusum control charts in the presence of correlation

Cited by 80 publications

References 36 publications

Optimal Design of Second-Order Linear Filters for Control Charting

Optimal Design of Second-Order Linear Filters for Control Charting

Inference for post-change parameters after sequential CUSUM test under AR(1) model

Eliminating the influence of serial correlation on statistical process control charts using trend free pre-whitening (TFPW) method

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