Variable Sampling Interval<i>X̄</i>Charts in the Presence of Correlation

Reynolds, Marion R.; Arnold, Jesse C.; Baik, Jai Wook

doi:10.1080/00224065.1996.11979633

Cited by 72 publications

(51 citation statements)

References 29 publications

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“…It is well-known that when the observations are independent the X chart with variable sampling interval detects process shifts faster than the X chart with fixed sampling interval. Reynolds, Arnold & Baik (1996) worked with autocorrelated observations and obtained the same conclusion. In this paper, we study the efficiency of the double sampling X chart when the observations follow a first order autoregressive model and the samples are formed according to the rational subgroup concept.…”

Section: Introductionsupporting

confidence: 52%

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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Section: Introductionsupporting

confidence: 52%

Double sampling control chart for a first order autoregressive process

2008

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“…Firstly, the model for the VSI process of individual observations which is used in Reynolds et al 19 is reviewed. Suppose that observations are taken from a process at regularly spaced sampling time, and let X k represent the observation taken at sampling time k. Assume that X k can be represented as…”

Section: Statistical Models For An Autocorrelated Processmentioning

confidence: 99%

“…The autocorrelated models under investigation are similar to those of Reynolds et al 19 , but allow for varying the sample size and are briefly introduced in the next section. The VSIFT and VSRFTX charts which are inclusively called the variable sampling scheme at fixed times (VSFT)X charts are described in Section 3.…”

Section: Introductionmentioning

confidence: 99%

“…(iv) What is the degree of advantage of a VSR chart for an autocorrelated process and how to determine a proper VSR scheme and to decide its parameters. Reynolds et al 19 considered the FSI and VSIX charts under a first-order autoregressive (AR(1)) model with additional random error. They showed that the correlation between successive means had a significant effect on the properties of both FSI and VSIX charts.…”

Section: Introductionmentioning

confidence: 99%

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Monitoring autocorrelated processes using variable sampling schemes at fixed‐times

Zou

Wang

Tsung

2007

Quality & Reliability Eng

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Traditional control charts for process monitoring are based on taking samples of fixed size from the process using a fixed sampling interval. A recent development in control charts is the use of adaptive control charts, i.e. the variable sampling interval (VSI) and variable sampling size charts. This paper extends this idea to the autocorrelated process. We consider a time series model which is a first-order autoregressive process plus a random error. With variable intervals, the sampling time may be inconvenient, so using only two intervals, referred to as 'variable sampling interval at fix times' makes the method easier to use in practice. The sampling rate can also be adjusted by the number of samples collected, VSRFT, for 'variable sampling rate at fixed times'. We study what we call 'variable sampling at fixed times', VSFT, which includes both VSIFT and VSRFT schemes, using a Markov chain model and integral equations. We show that our methods detect process shifts faster, on average, than fixed sampling X-bar charts, and at least comparable detection ability with the less practical VSI charts.

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“…A idéia de variar o intervalo entre retirada de amostras foi primeiro explorada com os gráficos X (REYNOLDS, et al, 1988;RUNGER & PIGNATIELLO, 1991;AMIN & MILLER, 1993;RUNGER & MONTGOMERY, 1993;BAXLEY, 1995;REYNOLDS, ARNOLD & BAIK, 1996;, mas logo se estendeu para outros gráficos (REYNOLDS, AMIN & ARNOLD, 1990;SACCUCCI, AMIN & LUCAS, 1992). Por sua vez, PRABHU, RUNGER & KEATS (1993) e COSTA, (1994 estudaram os gráficos X com o tamanho das amostras variável.…”

Section: Introductionunclassified

Gráficos de controle X para processos robustos

Costa

1998

Gest. Prod.

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Resumo O avanço tecnológico tem tornado os processos produtivos cada vez mais robustos (robustos no sentido de produzirem itens cada vez mais iguais). Neste contexto, pequenas alterações no processo podem ser críticas, devendo portanto ser eliminadas com rapidez. Tradicionalmente, são utilizados os gráficos das somas acumuladas ou das médias móveis para controlar tais processos. O objetivo deste trabalho é mostrar que os gráficos de Shewhart também podem ser utilizados para controlar processos robustos, bastando variar seus parâmetros de projeto de maneira apropriada.Palavras-chave: processos robustos, controle de processos, gráficos de Shewhart com parâmetros variáveis.

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Variable Sampling IntervalX̄Charts in the Presence of Correlation

Cited by 72 publications

References 29 publications

Double sampling control chart for a first order autoregressive process

Double sampling control chart for a first order autoregressive process

Monitoring autocorrelated processes using variable sampling schemes at fixed‐times

Gráficos de controle X para processos robustos

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