Data driven choice of control charts

Albers, Willem; Kallenberg, W.C.M.; Nurdiati, Sri

doi:10.1016/j.jspi.2004.07.003

Cited by 16 publications

(22 citation statements)

References 20 publications

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“…Note that for > 1, the moment generating function of X i , having a normal power distribution with parameter , does not exist, and therefore the results of Theorem 3.1 and its proof are not standard. For a proof of this theorem we refer to Albers et al (2006). …”

Section: Estimationmentioning

confidence: 99%

“…Since F X n−r and F X n−r+1 are distributed as U r+1 and U r , respectively, we get Eg P n = P V = 1 Eg U r+1 + P V = 0 Eg U r = Eg U r + P V = 1 Eg U r+1 − Eg U r = g p From a practical point of view the nonparametric control chart is still questionable for r = 0, because it implies that with positive probability we will never get an out-of-control signal! Therefore a modification of the nonparametric control in case r = 0 is presented in Albers et al (2006). We do not discuss this modification here.…”

Section: Biasmentioning

confidence: 99%

“…The particular choice of the boundaries is partly by theoretical arguments (see Theorem 5.1) but also based on our simulation experience. For a more extensive discussion we refer to Albers et al (2006).…”

Section: Combined Control Chartmentioning

confidence: 99%

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Shewhart Control Charts in New Perspective

Albers

Kallenberg

2007

Sequential Analysis

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The effects of estimating parameters and the violation of the assumption of normality when dealing with control charts are discussed. Corrections for estimating errors and extensions of the normal control chart to parametric and nonparametric charts are investigated. The underlying theory is extensively discussed, including the choice of a suitable parametric family containing the normal family. It turns out that classical contamination families like random or deterministic mixtures do not give a suitable solution here. The socalled normal power family leads to an acceptable family, as it is intimately connected to the problem at hand of modeling and estimating an extreme quantile. When the underlying distribution cannot be modeled sufficiently accurately by the normal power family, the nonparametric control chart comes into the picture. A data-driven procedure makes the choice between the three different charts. When the nonparametric chart turns up, a large number of Phase I observations are needed. When such a large sample size is not available, it may be preferred to replace the individual chart by a grouped one. The new minimum chart is recommended in that case.

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Section: Estimationmentioning

confidence: 99%

Section: Biasmentioning

confidence: 99%

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Shewhart Control Charts in New Perspective

Albers

Kallenberg

2007

Sequential Analysis

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“…For example, Bakir (2006) has constructed a Shewhart-type control chart using a signed-rank statistic, Chakraborti and Eryilmaz (2007) have considered an alternative class of charts based on the same statistic, while Albers et al (2006) have used a suitably modified version of a nonparametric control chart; for an overview of distribution-free control charts for continuous variables, interested readers are referred to Chakraborti et al (2001).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

Balakrishnan

Triantafyllou

Koutras

2009

Journal of Statistical Planning and Inference

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“…A next step will be to use the data in deciding whether to use a parametric control chart or a nonparametric one. This latter topic is treated in Albers, Kallenberg and Nurdiati (2002c).…”

Section: Introductionmentioning

confidence: 99%

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

Albers

Kallenberg

2004

Journal of Applied Statistics

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Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.

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Data driven choice of control charts

Cited by 16 publications

References 20 publications

Shewhart Control Charts in New Perspective

Shewhart Control Charts in New Perspective

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

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