Economic-statistical design of the chart used to control a wandering process mean using genetic algorithm

Franco, Bruno Chaves; Costa, Antônio Fernando Branco; Machado, Marcela Aparecida Guerreiro

doi:10.1016/j.eswa.2012.05.034

Cited by 21 publications

(13 citation statements)

References 35 publications

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“…) denotes the standardized mean vector shift, see (Wu & Makis, 2008) and (Franco et al, 2012) . Without loss of generalization, we consider μ 01 = μ 02 = 0.…”

Section: The Effect Of the Auto-and Cross-correlation On The Performamentioning

confidence: 99%

“…Lin, Chou, Wang, and Liu (2012) considered the economic design of the autoregressive moving average (ARMA) control chart, which has been shown to be suitable for monitoring series of autocorrelated data. Franco, Costa, and Machado (2012) considered the first-order autoregressive model, AR (1), to describe the wandering behavior of the process mean, and they used Duncan's model to obtain the optimum values of the X chart parameters. Costa and Machado (2011) also used the AR (1) model to investigate the effect of the wandering behavior of the process mean on the performance of the variable parameter X chart and on the performance of the double sampling X chart.…”

Section: Introductionmentioning

confidence: 99%

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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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“…) denotes the standardized mean vector shift, see (Wu & Makis, 2008) and (Franco et al, 2012) . Without loss of generalization, we consider μ 01 = μ 02 = 0.…”

Section: The Effect Of the Auto-and Cross-correlation On The Performamentioning

confidence: 99%

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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“…For brevity, instead of elaborating them in detail, we recommend the books, namely, Montgomery for a broad overview and Qiu for more rigorous statistical treatments of the subject. There are many cost‐efficient monitoring schemes which are also capable of controlling type I error probability (see Yang and Rahim, Chen and Cheng, Niaki et al, Franco et al, Mohammadian and Amiri, Liu et al, Naderi et al, Saadatmelli et al, among others). Most of these works are, however, in the parametric context and adopt a specific distribution for the process characteristic(s).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric cost‐minimized Shewhart‐type process monitoring with restricted false alarm probability

Mukherjee

2019

Quality & Reliability Eng

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Traditional Duncan-type models for cost-efficient process monitoring often inflate type I error probability. Nevertheless, controlling the probability of type I error or false alarms is one of the key issues in sequential monitoring of specific process characteristics. To this end, researchers often recommend economic-statistical designs. Such designs assign an upper bound on type I error probability to avoid excessive false alarms while achieving cost optimality. In the context of process monitoring, there is a plethora of research on parametric approaches of controlling type I error probability along with the cost optimization. In the nonparametric setup, most of the existing works on process monitoring address one of the two issues but not both simultaneously. In this article, we present two distribution-free cost-efficient Shewhart-type schemes for sequentially monitoring process location with restricted false alarm probability, based, respectively, on the sign and Wilcoxon rank-sum statistics. We consider the one-sided shift in location parameter in an unknown continuous univariate process. Nevertheless, one can easily extend our proposed schemes to monitor the two-sided process shifts. We evaluate and compare the actual performance of the two monitoring schemes employing extensive computer simulation based on Monte Carlo. We investigate the effects of the size of the reference sample and the false alarm constraint. Finally, we provide two illustrative examples, each based on a realistic situation in the industry.

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“…Alternatives as the use of heuristic methods as Genetic Algorithms [1,2,13], Tabu-Search [14], and Greedy Algorithms [15] have been considered to estimate the optimal solution. Other non-heuristic methods as Fuzzy Logic and Neural Networks have also been adapted for this purpose.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the effect of non-normality on the solution space for the economic statistical design of X-bar control charts

Caballero‐Morales

Rahim

2015

2015 International Conference on Industrial Engineering and Operations Management (IEOM)

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the assumption of normality is commonly considered when designing X-bar control charts. However in practice sometimes the measurements of the quality attribute are not normally distributed, especially when the size of the sample is small. For the economic statistical design of X-bar control charts the assumption of non-normality is important as it has significant effect on the estimation of the chart's parameters (n,h,k). In this paper the effect of non-normality on the solution space for the economic statistical design of X-bar control charts is studied. Considering constant sampling intervals it was observed that the assumption of non-normality reduces the valid range of k. In contrast for variable sampling intervals it was observed that the non-normal assumption has a significant effect on the lower bound for h. By understanding how the solution space is restricted by the non-normality assumption more effective solving algorithms for this problem can be developed.

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Economic-statistical design of the chart used to control a wandering process mean using genetic algorithm

Cited by 21 publications

References 35 publications

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

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

Nonparametric cost‐minimized Shewhart‐type process monitoring with restricted false alarm probability

Analyzing the effect of non-normality on the solution space for the economic statistical design of X-bar control charts

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