Some Comments Regarding the Synthetic Chart

Machado, Marcela Aparecida Guerreiro; Costa, Antônio Fernando Branco

doi:10.1080/03610926.2012.683128

Cited by 27 publications

(49 citation statements)

References 23 publications

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“…The NSS simple and improved synthetic charts are denoted here as S1 (first proposed by Wu and Spedding) and IS1 (first proposed by Wu et al), respectively. Similarly, the SSS, RSS, MSS, simple, and improved synthetic charts are denoted here as S2 (by Davis and Woodall) and IS2, S3 (by Machado and Costa) and IS3 (by Machado and Costa), and S4 (by Shongwe and Graham) and IS4 (by Shongwe and Graham), respectively. Using Figure , Table is constructed to distinctly show the different regions that are used to differentiate between these synthetic‐type charts.…”

Section: Design Of the Shewhart Synthetic Chartsmentioning

confidence: 99%

An overview of synthetic‐type control charts: Techniques and methodology

Rakitzis

Chakraborti

Shongwe

et al. 2019

Quality & Reliability Eng

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In this paper, we provide an overview of a class of control charts called the synthetic charts. Synthetic charts are a combination of a traditional chart (such as a Shewhart, CUSUM, or EWMA chart) and a conforming run‐length (CRL) chart. These charts have been considered in order to maintain the simplicity and improve the performance of small and medium‐sized shift detection of the traditional Shewhart charts. We distinguish between different types of synthetic‐type charts currently available in the literature and highlight how each is designed and implemented in practice. More than 100 publications on univariate and multivariate synthetic‐type charts are reviewed here. We end with some concluding remarks and a list of some future research ideas.

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Section: Design Of the Shewhart Synthetic Chartsmentioning

confidence: 99%

An overview of synthetic‐type control charts: Techniques and methodology

Rakitzis

Chakraborti

Shongwe

et al. 2019

Quality & Reliability Eng

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“…The ZS run‐length is the number of sampling points at which the chart first signals given it begins in some initial state; that is, we assume that the mean shift always takes place at the beginning of the process, and thus, all sample points within the span are taken under the OOC condition. However, the SS run‐length is the number of sampling points at which the chart first signals given that the process begins and stays IC for a very long time; then at some random time, an OOC signal is observed; see Champ, Davis and Woodall, Zhang and Wu, and Machado and Costa . This is further discussed in the Appendix.…”

Section: Operation and Design Considerationsmentioning

confidence: 99%

“…As explained in Figure , the synthetic‐type and runs‐type charts may be classed into four categories, that is, NSS, SSS, RSS, and MSS. The NSS, SSS, RSS, and MSS synthetic

\overset{X}{true}

charts were proposed by Wu and Spedding, Davis and Woodall, Machado and Costa, and Shongwe and Graham – these are denoted by S1, S2, S3, and S4, respectively. The NSS, SSS, RSS, and MSS 2‐of‐( H + 1) RR

\overset{X}{true}

charts were proposed by Derman and Ross, Klein, adopted from Machado and Costa and Antzoulakos and Rakitzis – these are denoted by RR1, RR2, RR3, and RR4, respectively.…”

Section: Comparison With the 2‐of‐(h + 1) Runs‐rules And Synthetic Tmentioning

confidence: 99%

On the Performance of Shewhart-type Synthetic and Runs-rules Charts Combined with an X¯ Chart

Shongwe

Graham

2015

Qual. Reliab. Engng. Int.

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A synthetic ̅ chart is a combination of a conforming run-length chart and an ̅ chart, or equivalently, a 2-of-(H+1) runs-rules (RR) chart with a head-start feature. However, a synthetic ̅ chart combined with an ̅ chart is called a Synthetic-̅ chart. In this article, we build a framework for Shewhart Synthetic-̅ and improved RR (i.e. 1-of-1 or 2-of-(H+1) without head-start) charts by conducting an in-depth zero-state and steady-state study to gain insight into the design of different classes of these schemes and their performance using the Markov chain imbedding technique. More importantly, we propose a modified side-sensitive Synthetic-̅ chart, and then using overall performance measures we show that this new chart has a uniformly better performance than its Shewhart competitors. We also provide easy to use tables for each of the chart"s design parameters to aid practical implementation. Moreover, a performance comparison with their corresponding counterparts (i.e. synthetic ̅ and RR charts) is conducted.

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“…The vector S = D − 1 S C , where

\begin{matrix} center \\ center S_{C}^{'} = (C^{L - 1}, C^{L - 2}, & center \dots, C^{0}, 2 C^{L} / (1 - A), & center C^{0}, \dots, C^{L - 2}, C^{L - 1}) \end{matrix}

and D = 2 + 2 C + 2 C 2 + … + 2 C L /(1 − A ), with C = 2 A /(1 + A ). For more details, see Machado and Costa. When the side‐sensitive synthetic

\overset{X}{true}

control chart is integrated with the DS scheme, A = P (0).…”

Section: The Steady‐state Average Run Length Of the Side‐sensitive Symentioning

confidence: 99%

“…Wu and Spedding introduced the synthetic chart using L as the design parameter. According to Machado and Costa, the side‐sensitive synthetic chart performs better than the standard synthetic chart. In this article, we study the steady‐state properties of the standard synthetic and side‐sensitive synthetic DS

\overset{X}{true}

charts, named the SDS and SSDS

\overset{X}{true}

charts, respectively.…”

Section: Introductionmentioning

confidence: 99%

The steady‐state behavior of the synthetic and side‐sensitive synthetic double sampling charts

Costa

Machado

2014

Quality & Reliability Eng

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The steady‐state average run length is used to measure the performance of the recently proposed synthetic double sampling trueX¯ chart (synthetic DS chart). The overall performance of the DS trueX¯ chart in signaling process mean shifts of different magnitudes does not improve when it is integrated with the conforming run length chart, except when the integrated charts are designed to offer very high protection against false alarms, and the use of large samples is prohibitive. The synthetic chart signals when a second point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it; with the side‐sensitive feature, the synthetic chart does not signal when they fall on opposite sides of the centerline. We also investigated the steady‐state average run length of the side‐sensitive synthetic DS trueX¯ chart. With the side‐sensitive feature, the overall performance of the synthetic DS trueX¯ chart improves, but not enough to outperform the non‐synthetic DS trueX¯ chart. Copyright © 2014 John Wiley & Sons, Ltd.

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Some Comments Regarding the Synthetic Chart

Cited by 27 publications

References 23 publications

An overview of synthetic‐type control charts: Techniques and methodology

An overview of synthetic‐type control charts: Techniques and methodology

On the Performance of Shewhart-type Synthetic and Runs-rules Charts Combined with an X¯ Chart

The steady‐state behavior of the synthetic and side‐sensitive synthetic double sampling charts

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