Effect of measurement error and autocorrelation on the<i>X¯</i>chart

Costa, Antônio Fernando Branco; Castagliola, Philippe

doi:10.1080/02664760903563627

Cited by 91 publications

(123 citation statements)

References 14 publications

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“…But, in many industrial scenarios, there often exist significant measurement errors that affect the performance of control charts. Since Bennet (1954) investigated the effect of measurement errors on the ShewhartX chart, there are many studies about the actual performance of various control charts in the presence of measurement error, for further details see for instance: Kanazuka (1986), , Linna, Woodall, and Busby (2001), Maravelakis (2004), Costa and Castagliola (2011), Maravelakis (2012). Recently, Hu et al (2015) investigated the performance of the syntheticX chart when measurement errors exist using a linear covariate error model and they showed that the performance of the syntheticX chart is significantly affected in the presence of measurement error.…”

Section: Introductionmentioning

confidence: 99%

The performance of the Shewhart-RZ control chart in the presence of measurement error

Tran

Castagliola

Celano

2016

International Journal of Production Research

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Recent literature about quality control has investigated the continuous surveillance of the ratio of two normal random variables under the assumption of no measurement error. However, in practice, measurement errors always exist in quality control applications and may considerably affect the performance of control charts. In this paper, the performance of the Shewhart-RZ control chart is investigated in the presence of a measurement error and modelled by a linear covariate error model. Several figures and tables are generated and commented to show the statistical performance of the Shewhart-RZ control chart for different sources of the measurement error. Two examples illustrate the use of this chart on a quality control problem simulated from the food industry and a real industrial case from a plant treating batteries for recyclement.

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Section: Introductionmentioning

confidence: 99%

The performance of the Shewhart-RZ control chart in the presence of measurement error

Tran

Castagliola

Celano

2016

International Journal of Production Research

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“…Regarding to the correlation, if the de- pendence among X observations and among Y observations are the same (or close), that is, a ∼ = b, T 2 chart has a better overall performance when the variables X and Y are highly correlated. The authors are currently investigating the use of the skip sampling strategy proposed by Costa and Castagliola (2011) and the mixed sampling strategy proposed by Franco et al (2013) to reduce the negative effect of the autocorrelations on the statistical performance of the T 2 control chart. λ 2 (n) = n 3 δ 2 2 (b − 1) 4 (b + 1) b 3 (n 2 ρ 2 − n 2 + 2nρ 2 + ρ 2 ) − b 2 (n 2 ρ 2 − n 2 + 2nρ 2 − 2n) + b 2n+2 ρ 2 − 2b n+3 ρ 2 − 2b n+2 ρ 2 + b 2n+3 ρ 2 − 2b n+1 n + 2b n+2 n + n 2 ρ 2 − n 2 + 2b n+1 nρ 2 − 2b n+3 nρ 2 −1 (B.2)…”

Section: Discussionmentioning

confidence: 99%

“…To reduce the negative effect of autocorrelation on the statistical performance of the Shewhart X control chart, Costa and Castagliola (2011) proposed a sampling strategy denoted 's-skip'. According to this strategy, samples are obtained by collecting one item from the production line and then skipping s consecutive items before selecting the next one.…”

Section: Introductionmentioning

confidence: 99%

The effect of the autocorrelation on the performance of the T 2 chart

Leoni

Costa

Machado

2015

European Journal of Operational Research

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a b s t r a c tIn this article, we consider the T 2 control chart for bivariate samples of size n with observations that are not only cross-correlated but also autocorrelated. The cross covariance matrix of the sample mean vectors is derived with the assumption that the observations are described by a multivariate first order autoregressive model -VAR (1). The combined effect of the correlation and autocorrelation on the performance of the T 2 chart is also investigated. Earlier studies proved that changes in only one variable are detected faster when the variables are correlated. This result extends to the case that one or both variables are also autocorrelated.

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“…See, for example, (Haiyu, 2010;Costa and Castagliola, 2011;Tasdemir, 2012;Goswami and Dutta, 2013;Singh and Prajapati, 2013).…”

Section: Introductionmentioning

confidence: 99%

Model Building for Autocorrelated Process Control: An Industrial Experience

Djauhari

Lee

Ismail³

2014

American Journal of Applied Sciences

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We show that many time series data are governed by Geometric Brownian Motion (GBM) law. This motivates us to propose a procedure of time series model building for autocorrelated process control that might consist of two steps. First, we test whether the process data are governed by GBM law. If it is affirmative, the appropriate model is directly given by the properties of that law. Otherwise, we go to the standard practice at the second step where the best model is constructed by using ARIMA method. An industrial example will be reported to demonstrate the advantages of that procedure. In that example, a comparison study with ARIMA method will be reported to illustrate the effectiveness and efficiency of the GBM-based model building.

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Effect of measurement error and autocorrelation on theX¯chart

Cited by 91 publications

References 14 publications

The performance of the Shewhart-RZ control chart in the presence of measurement error

The performance of the Shewhart-RZ control chart in the presence of measurement error

The effect of the autocorrelation on the performance of the T 2 chart

Model Building for Autocorrelated Process Control: An Industrial Experience

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