2008
DOI: 10.1590/s0101-74382008000300008
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Double sampling control chart for a first order autoregressive process

Abstract: 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-subg… Show more

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Cited by 15 publications
(7 citation statements)
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“…They studied for a variable sample size and sampling interval. Claro et al (2008) proposed the double sampling (DS) X control chart for monitoring processes in which the observations followed a first order autoregressive model, AR (1). They considered sampling intervals that are sufficiently long to meet the rational subgroup concept.…”
Section: Detection Of Shift In Process Meanmentioning
confidence: 99%
“…They studied for a variable sample size and sampling interval. Claro et al (2008) proposed the double sampling (DS) X control chart for monitoring processes in which the observations followed a first order autoregressive model, AR (1). They considered sampling intervals that are sufficiently long to meet the rational subgroup concept.…”
Section: Detection Of Shift In Process Meanmentioning
confidence: 99%
“…If the results are not clear‐cut, a second random sample is selected and inspected and a final decision is taken using the results of the two samples (Balakrishnan et al, 2006). Claro et al (2008) proposed the double sampling control chart for the autoregressive process. Torng and Lee (2009) discussed the performances of a double sampling (DS) trueX0.25em¯ chart under nonnormality assumptions in comparison with a Shewhart trueX0.25em¯ chart.…”
Section: Introductionmentioning
confidence: 99%
“…Some of these models are known as autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), etc; see Box et al for more thorough discussion on these. In this paper, we only consider the well‐known first‐order AR model (ie, AR(1)) as a starting point (other models will be discussed in upcoming articles) and because according to Alwan and Radson, this is the most commonly used time series model in SPM applications; see also Wardell et al, Runger and Willemain, Claro et al, Kazemzadeh et al, Costa and Machado, Chang and Wu, Keramatpour et al, Franco et al, Hu and Sun, Osei‐Aning et al, Garza‐Venegas et al, Shongwe et al, Ahmad et al, etc, for additional indication that AR(1) is the most used model in SPM due to its simplicity as compared with other stationary time series processes.…”
Section: Introductionmentioning
confidence: 99%