Synthetic-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si844.gif" overflow="scroll"><mml:mover accent="true"><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:math>control charts optimized for in-control and out-of-control regions

Aparisi, Francisco; Luna, Marco A.

doi:10.1016/j.cor.2009.02.024

Cited by 28 publications

(14 citation statements)

References 21 publications

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“…This arises when most of the shifts cluster to the high end, or when all small shifts have been truncated to avoid over-correction that may introduce extra variability into the process (Woodall 1985, Aparisi andDe Luna 2009). In this case, the AEQL values produced by both X chart and optimal 3-CUSUM chart become larger.…”

Section: Performance Comparison Under Different Probability Distributmentioning

confidence: 91%

The X control chart for monitoring process shifts in mean and variance

Yang

Lee

et al. 2012

International Journal of Production Research

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Control charts are widely used in statistical process control (SPC) to monitor the quality of products or production processes. When dealing with a variable (e.g., the diameter of a shaft, the hardness of a component surface), it is necessary to monitor both its mean and variability (Montgomery 2009[Montgomery, D.C., 2009. Introduction to statistical quality control. New York: John Wiley & Sons.]). This article studies and compares the overall performances of the X chart and the 3-CUSUM chart for this purpose. The latter is a combined scheme incorporating three individual CUSUM charts and is considered as the most effective scheme for detecting mean shift and/or standard deviation shift in current SPC literature. The results of the performance studies reveal two interesting findings: (1) the best sample size n for an " X chart is always n ¼ 1, in other words, the simplest X chart (i.e., the " X chart with n ¼ 1) is the most effective "X chart for detecting and/or ; (2) the simplest X chart often outperforms the 3-CUSUM chart from an overall viewpoint unless the latter is redesigned by a difficult optimisation procedure. However, even the optimal 3-CUSUM chart is only slightly more effective than the X chart unless the process shift domain is quite small. Since the X chart is very simple to understand, implement and design, it may be more suitable in many SPC applications, in which both the mean and variance of a variable need to be monitored.

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Section: Performance Comparison Under Different Probability Distributmentioning

confidence: 91%

The X control chart for monitoring process shifts in mean and variance

Yang

Lee

et al. 2012

International Journal of Production Research

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“…Thus, the three charts are compared based on their sample-size performance. Note that only moderate and large are considered in this paper because in many real industrial applications, small shifts in the process are usually not desirable to be detected in order to avoid too frequent process interruptions [5], [29].…”

Section: Comparative Studiesmentioning

confidence: 99%

Optimal Designs of the Median Run Length Based Double Sampling X̄ Chart for Minimizing the Average Sample Size

2013

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Designs of the double sampling (DS) chart are traditionally based on the average run length (ARL) criterion. However, the shape of the run length distribution changes with the process mean shifts, ranging from highly skewed when the process is in-control to almost symmetric when the mean shift is large. Therefore, we show that the ARL is a complicated performance measure and that the median run length (MRL) is a more meaningful measure to depend on. This is because the MRL provides an intuitive and a fair representation of the central tendency, especially for the rightly skewed run length distribution. Since the DS chart can effectively reduce the sample size without reducing the statistical efficiency, this paper proposes two optimal designs of the MRL-based DS chart, for minimizing (i) the in-control average sample size (ASS) and (ii) both the in-control and out-of-control ASSs. Comparisons with the optimal MRL-based EWMA and Shewhart charts demonstrate the superiority of the proposed optimal MRL-based DS chart, as the latter requires a smaller sample size on the average while maintaining the same detection speed as the two former charts. An example involving the added potassium sorbate in a yoghurt manufacturing process is used to illustrate the effectiveness of the proposed MRL-based DS chart in reducing the sample size needed.

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“…GAs have proved to be an efficient tool to optimise quality control charts. See, for example, Chen (2007), Kaya (2009) and Aparisi and De Luna (2009). In order to maximise the performance of a GA, a careful optimisation of its parameters has been done.…”

Section: Optimisation Of the Ewma Lcp Control Chartmentioning

confidence: 99%

Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control

García-Bustos

Aparisi

Epprecht

2014

International Journal of Production Research

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In this paper, we propose a new process control chart for monitoring correlated Poisson variables, the EWMA LCP chart. This chart is the exponentially weighted moving average (EWMA) version of the recently proposed LCP chart. The latter is a Shewhart-type control chart whose control statistic is a linear combination of the values of the different Poisson variables (elements of the Poisson vector) at each sampling time. As a Shewhart chart, it is effective at signalling large process shifts but is slow to signal smaller shifts. EWMA charts are known to be more sensitive to small and moderate shifts than their Shewhart-type counterparts, so the motivation of the present development is to enhance the performance of the LCP chart by the incorporation of the EWMA procedure to it. To ease the design of the EWMA LCP chart for the end user, we developed a user-friendly programme that runs on Windows© and finds the optimal design of the chart, that is, the coefficients of the linear combination as well as the EWMA smoothing constant and chart control limits that together minimise the out-of-control ARL under a constraint on the in-control ARL. The optimization is carried out by genetic algorithms where the ARLs are calculated through a Markov chain model. We used this programme to evaluate the performance of the new chart. As expected, the incorporation of the EWMA scheme greatly improves the performance of the LCP chart.

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Synthetic-X¯control charts optimized for in-control and out-of-control regions

Cited by 28 publications

References 21 publications

The X control chart for monitoring process shifts in mean and variance

The X control chart for monitoring process shifts in mean and variance

Optimal Designs of the Median Run Length Based Double Sampling X̄ Chart for Minimizing the Average Sample Size

Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control

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