Combined double sampling and variable sampling interval X chart

Carot, V.; Vivas, José Manuel Jabaloyes; Carot, T.

doi:10.1080/00207540210128260

Cited by 59 publications

(44 citation statements)

References 16 publications

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“…In Tables 8 and 9, the results of this analysis are reported with respect to different scenarios. Furthermore, Table 9 shows a comparison with C U S U M and E W M A charts, in the same way as suggested by Carot et al [24]. …”

Section: Computational Resultsmentioning

confidence: 74%

“…The positive effect of run rules is Once the positive effects of adding run rules to adaptive schemes with variable sample size and/or sampling interval have been demonstrated, a further interesting analysis examines the comparison with other kinds of control charts. In a recent publication, Carot et al [24] proposed a chart, denoted as DSVSI, derived from the combination of a double sampling .~ chart (DS) with a variable sampling interval (VSI) approach. They show how such a new hybrid scheme outperforms the tradition adaptive and run rule Shewhart charts.…”

Section: Computational Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Statistical design of variable sample size and sampling interval $$\bar X$$ control charts with run rulescontrol charts with run rules

Celano

Costa

Fichera

2006

Int J Adv Manuf Technol

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In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.

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Section: Computational Resultsmentioning

confidence: 74%

Section: Computational Resultsmentioning

confidence: 99%

Statistical design of variable sample size and sampling interval $$\bar X$$ control charts with run rulescontrol charts with run rules

Celano

Costa

Fichera

2006

Int J Adv Manuf Technol

View full text Add to dashboard Cite

show abstract

“…Torng and Lee [15] studied the DS X chart when the observations follow non-normal distributions. The combined DS and VSI (DSVSI) X chart was proposed by Carot et al [16], who claimed that the DSVSI X chart is more sensitive to small and moderate process mean shifts. Inspired by Carot et al [16], Torng et al [17] furthered this research and discussed the DSVSI X chart under non-normality.…”

Section: Introductionmentioning

confidence: 99%

“…The combined DS and VSI (DSVSI) X chart was proposed by Carot et al [16], who claimed that the DSVSI X chart is more sensitive to small and moderate process mean shifts. Inspired by Carot et al [16], Torng et al [17] furthered this research and discussed the DSVSI X chart under non-normality. Then Lee et al [18] proposed the economic design of the DSVSI X chart.…”

Section: Introductionmentioning

confidence: 99%

Exact Run Length Distribution of the Double Sampling X-Bar Chart With Estimated Process Parameters

Teoh

Fun

Teh

et al. 2016

SAJIE

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Since the run length distribution is generally highly skewed, a significant concern about focusing too much on the average run length (ARL) criterion is that we may miss some crucial information about a control chart's performance. Thus it is important to investigate the entire run length distribution of a control chart for an in-depth understanding before implementing the chart in process monitoring. In this paper, the percentiles of the run length distribution for the double sampling (DS) X chart with estimated process parameters are computed. Knowledge of the percentiles of the run length distribution provides a more comprehensive understanding of the expected behaviour of the run length. This additional information includes the early false alarm, the skewness of the run length distribution, and the median run length (MRL). A comparison of the run length distribution between the optimal ARL-based and MRL-based DS X chart with estimated process parameters is presented in this paper. Examples of applications are given to aid practitioners to select the best design scheme of the DS X chart with estimated process parameters, based on their specific purpose. OPSOMMINGAangesien die lopielengte verdeling in die algemeen baie skeef is, bestaan daar kommer oor die gebruik van die gemiddelde lopielengte (ARL) kriteria, omdat kritiese informasie op die beheerkaart gemis mag word. Dit is dus belangrik om die totale lopielengte verdeling van 'n beheerkaart te ondersoek, voordat die kaart geïmplementeer word. In hierdie artikel word die persentiele van die lopielengte verdeling van die dubbelmonster (DS) � kaart met geskatte prosesparameters bereken. Kennis van die persentiele van die lopielengte verdeling gee 'n meer omvattende verstaan van die verwagte lopielengte vertoning. Dié addisionele informasie sluit die vroeë vals alarm, die skeefheid van die verdeling en die mediaan van die lopielengte (MRL) in. 'n Vergelyking van die lopielengte verdeling tussen optimale ARLgebaseerde en MRL-gebaseerde DS � kaart met geskatte proses parameters word voorgehou. Voorbeelde word ook voorgehou om beoefenaars te help om die beste weergawe van die DS � kaart met geskatte proses parameters vir hul toepassing te kies.

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“…Considerable efforts have already been undertaken in the research of the statistical properties of the adaptive Shewhart charts with Variable Sampling Interval (VSI) (Reynolds, 1996;Runger & Montgomery, 1993); with Variable Sample Size (VSS) (Prabhu, Runger, Keats & Croasdale, 1993;Costa, 1994;Costa & Rahim, 2004), and with the Variable Sampling Interval and Variable Sample Size (VSSI) (Costa, 1997(Costa, , 1998a, 1999 a/b/c; Carot, Jabaloyes & Carot, 2002). Another alternative used to improve the performance of the traditional Shewhart charts is the Double Sampling (DS) procedure (Croasdale, 1974;Daudin, 1992).…”

Section: Introductionmentioning

confidence: 99%

Double sampling control chart for a first order autoregressive process

2008

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In this paper we propose the Double Sampling X control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling X chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.Keywords: autocorrelation; double sampling; statistical process control. ResumoNeste artigo propomos o gráfico de controle X de amostragem dupla para monitoramento de processos nos quais as observações seguem um modelo autoregressivo de primeira ordem. Nós consideramos intervalos de amostragem suficientemente longos em linha com o conceito de subgrupos racionais. O gráfico de controle X de amostragem dupla é substancialmente mais eficiente que o Gráfico de Shewhart e do que o Gráfico com Amostra de Tamanho Variável. Para estudar as propriedades destes gráficos nós derivamos expressões de forma-fechada para o Numero Médio de Amostras até o Sinal (NMA) levando em conta a correlação dentro do subgrupo. Os resultados numéricos mostram que esta correlação tem impacto significante sobre as propriedades do gráfico.Palavras-chave: autocorrelação; amostragem dupla; controle estatístico do processo.

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Combined double sampling and variable sampling interval X chart

Cited by 59 publications

References 16 publications

Statistical design of variable sample size and sampling interval $$\bar X$$ control charts with run rulescontrol charts with run rules

Statistical design of variable sample size and sampling interval $$\bar X$$ control charts with run rulescontrol charts with run rules

Exact Run Length Distribution of the Double Sampling X-Bar Chart With Estimated Process Parameters

Double sampling control chart for a first order autoregressive process

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