New Corrections for Old Control Charts

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

doi:10.1081/qen-200063498

Cited by 30 publications

(30 citation statements)

References 7 publications

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“…In this section, we assess the performance of the correction factors derived by Albers and Kallenberg (2005). First, we extend their work to subgroup control charts and then, based on simulations, we assess the accuracy of the proposed correction factors.…”

Section: Albers and Kallenberg's Correction Factorsmentioning

confidence: 99%

“…In addition, we derive new correction factors and compare their performance. It will be shown that our newly proposed correction factors outperform those of Albers and Kallenberg (2005).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we derive new corrections for the Shewhart X andX control charts to achieve a desired unconditional ARL. Although Albers and Kallenberg (2005) derived correction factors for the same objective function, they have only considered the individuals chart. Therefore, we extend their approach for the ShewhartX control chart.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, the performance of the correction factors of Albers and Kallenberg (2005) is assessed. Next, in Section 4 we describe the derivation of the newly proposed correction factors, and compare their performance.…”

Section: Introductionmentioning

confidence: 99%

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Correction factors for Shewhart and control charts to achieve desired unconditional ARL

Goedhart

Schoonhoven

Does

2016

International Journal of Production Research

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In this paper we derive correction factors for Shewhart control charts that monitor individual observations as well as subgroup averages. In practice, the distribution parameters of the process characteristic of interest are unknown and, therefore, have to be estimated. A well-known performance measure within Statistical Process Monitoring is the expectation of the average run length (ARL), defined as the unconditional ARL. A practitioner may want to design a control chart such that, in the in-control situation, it has a certain expected ARL. However, accurate correction factors that lead to such an unconditional ARL are not yet available. We derive correction factors that guarantee a certain unconditional in-control ARL. We use approximations to derive the factors and show their accuracy and the performance of the control charts -based on the new factors -in out-of-control situations. We also evaluate the variation between the ARLs of the individually estimated control charts.

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Section: Albers and Kallenberg's Correction Factorsmentioning

confidence: 99%

“…In addition, we derive new correction factors and compare their performance. It will be shown that our newly proposed correction factors outperform those of Albers and Kallenberg (2005).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Correction factors for Shewhart and control charts to achieve desired unconditional ARL

Goedhart

Schoonhoven

Does

2016

International Journal of Production Research

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“…Hence it remains worthwhile to derive corrections to bring such stochastic character under control. This has e.g., been done for both normal and nonparametric IND, as well as for nonparametric MIN (see Albers and Kallenberg 2005a, 2008. Here we shall address this point for CUMIN as well.…”

Section: The Nonparametric Chartmentioning

confidence: 99%

CUMIN charts

Albers

Kallenberg

2008

Metrika

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Classical control charts are very sensitive to deviations from normality. In this respect, nonparametric charts form an attractive alternative. However, these often require considerably more Phase I observations than are available in practice. This latter problem can be solved by introducing grouping during Phase II. Then each group minimum is compared to a suitable upper limit (in the two-sided case also each group maximum to a lower limit). In the present paper it is demonstrated that such MIN charts allow further improvement by adopting a sequential approach. Once a new observation fails to exceed the upper limit, its group is aborted and a new one starts right away. The resulting CUMIN chart is easy to understand and implement. Moreover, this chart is truly nonparametric and has good detection properties. For example, like the CUSUM chart, it is markedly better than a Shewhart X -chart, unless the shift is really large.

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On the Use of the Expected ARL Metric for Control Charts Based on Estimated Parameters

Schoonhoven

2016

Quality & Reliability Eng

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At the origination of the Shewhart control chart, it was assumed that the process parameters were known. The in-control Average Run Length (ARL) and the probability of having a false alarm (P) were introduced as metrics to indicate the in-control performance. These two metrics are related when the process data are i.i.d. normally distributed: the ARL equals 1=P. When the process parameters are unknown and have to be estimated, a similar relation holds for each estimated control chart, but the relation between the expected ARL (the average of the ARLs of all possible estimated charts) and the expected P is different. Control charts based on estimates are often designed such that the in-control ARL equals a predefined value. This paper shows that the expected in-control ARL is a less suitable design criterion.

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New Corrections for Old Control Charts

Cited by 30 publications

References 7 publications

Correction factors for Shewhart and control charts to achieve desired unconditional ARL

Correction factors for Shewhart and control charts to achieve desired unconditional ARL

CUMIN charts

On the Use of the Expected ARL Metric for Control Charts Based on Estimated Parameters

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