Joint ―<i>X</i> and <i>R</i> Charts with Two‐stage Samplings

Costa, Antônio Fernando Branco; Rahim, M. A.

doi:10.1002/qre.578

Cited by 35 publications

(19 citation statements)

References 22 publications

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“…Consider an example based on Costa and Rahim 26 . Suppose that a company, which supplies shafts, is facing considerable losses due to the production of defective items.…”

Section: Illustrative Examplementioning

confidence: 99%

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An adaptive chart for monitoring the process mean and variance

Costa

Magalhães

2006

Quality & Reliability Eng

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Traditionally, anX chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptiveX and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the jointX and R charts with fixed or adaptive parameters, they are not reliable in identifying the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non-central chi-square statistic chart. This new chart is more effective than the adaptiveX and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects.

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“…Consider an example based on Costa and Rahim 26 . Suppose that a company, which supplies shafts, is facing considerable losses due to the production of defective items.…”

Section: Illustrative Examplementioning

confidence: 99%

“…For instance, Costa and Rahim 25,26 and Rahim and Costa 27 developed economic models for jointX and R charts. Gan 28 considered joint EWMA charts; Albin et al 29 studied an X chart and an EWMA chart for individual observations.…”

Section: Introductionmentioning

confidence: 99%

An adaptive chart for monitoring the process mean and variance

Costa

Magalhães

2006

Quality & Reliability Eng

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“…Gan 15 and Holmes and Mergen 16 study a joint EWMA using an elliptical and acceptance charts, respectively. Costa and Rahim 17 suggested a chart, which is in accordance with max-EWMA scheme using non-central chi-squared statistic for bilateral processes. The idea of Chen et al 13 was extended by Costa and Rahim 18 .…”

Section: Introductionmentioning

confidence: 95%

On the Performance of Control Charts for Simultaneous Monitoring of Location and Dispersion Parameters

Zaman

Riaz

Lee

2016

Quality & Reliability Eng

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A single control chart is very famous to control assignable causes that shift the process because of variations in parameters (e.g., location and dispersion). Simultaneous monitoring of processes is another popular approach used for the bilateral processes. In this study, we have proposed the mixed control charts for simultaneously monitoring of process location and dispersion parameters. We have used the idea of mixed exponential weighted moving average and cumulative sum charts and designed the charting structures for simultaneous monitoring. The proposals are compared with several existing counterparts. The comparisons reveal numerous advantages of the proposed charts over the other existing scheme. The practical application of the proposed charts is also highlighted using an illustrative example based on a real dataset.

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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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Joint ―X and R Charts with Two‐stage Samplings

Cited by 35 publications

References 22 publications

An adaptive chart for monitoring the process mean and variance

An adaptive chart for monitoring the process mean and variance

On the Performance of Control Charts for Simultaneous Monitoring of Location and Dispersion Parameters

Double sampling control chart for a first order autoregressive process

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