Average Run Lengths for Exponentially Weighted Moving Average Control Schemes Using the Markov Chain Approach

Saccucci, Michael S.; Lucas, James M.

doi:10.1080/00224065.1990.11979227

Cited by 87 publications

(42 citation statements)

References 2 publications

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“…The computation of the average run length for the EWMA mean control chart is more complicated. We use the Markov chain approach which has also been used by Saccucci and Lucas [25]. The ARL of the EWMA mean control chart depends on the control limits which, in turn, depend on the chosen sample size, the coefficient of control limit, and smoothing parameter.…”

Section: Economic Design Of Ewma Control Chart Using Lorenzen and Vanmentioning

confidence: 99%

“…Moreover, the costs of Table 14 Parameters of three scenarios in a manufacturing real case in tile production industry other scenarios under single scenario optimization are reported in order to be used in next comparisons. Note that to compute the ARL of the control chart, the Markov chain method proposed by Saccucci and Lucas [25] is used in which the number of intervals between control limits is assumed to be 51. After obtaining the optimum parameters for each scenario separately, the robust economic models of EWMA control chart by considering two robust approaches introduced in Eqs.…”

Section: Robust Economic Design Of Ewma Control Chartmentioning

confidence: 99%

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Robust economic and economic-statistical design of EWMA control chart

Amiri

Moslemi

Doroudyan

2014

Int J Adv Manuf Technol

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Uncertainty in the cost and process parameters is very common in practice. In this paper, we develop a scenariobased robust economic and economic-statistical design of exponentially weighted moving average control chart to account for economic and statistical criteria as well as the uncertainty. For this purpose, we use Lorenzen and Vance cost function for economic and economic-statistical design of an exponentially weighted moving average control chart in the real applications. Absolute robustness criterion which minimizes the worst-case scenario and also robust deviation which minimizes the deviation from the optimal solutions are applied to explore the robust approach for robust design of the exponentially weighted moving average control chart. The optimization models are solved by using the genetic algorithm. The performance of the proposed methods is illustrated through two numerical examples. Finally, the application of the proposed methods is illustrated in a real manufacturing case in the tile production industry.

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Section: Economic Design Of Ewma Control Chart Using Lorenzen and Vanmentioning

confidence: 99%

Section: Robust Economic Design Of Ewma Control Chartmentioning

confidence: 99%

Robust economic and economic-statistical design of EWMA control chart

Amiri

Moslemi

Doroudyan

2014

Int J Adv Manuf Technol

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“…This approach is commonly used in calculating the ARL of control charts (e.g., Saccucci and Lucas, 1990), and is described in more detail in Appendix A. In order to find the optimal solution, we first fix the sample size n and optimize (9) with respect to the other five decision variables.…”

Section: Computational Optimization Proceduresmentioning

confidence: 99%

Joint economic design of EWMA control charts for mean and variance

Serel

Moskowitz

2008

European Journal of Operational Research

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Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi's quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.

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“…Researches on the designs of various control charts may be traced back to 1960's and a lot of theoretical developments and applications on control charts can be still found in recent literatures, such as Haridy et al (2012), Chou et al (2013), Requeijo and Cordeiro (2013), Karaoglan and Bayhan (2014), Liu et al (2014). The control charts with exponentially weighted moving average (EWMA) scheme was first introduced by Roberts (1966) and had been shown to be effective for detecting small shifts in the mean of the process characteristic (e.g., see Saccucci and Lucas, 1990). From the statistical viewpoint, a moving average is a calculation to analyse data points by creating a series of averages of different subsets from the full data set.…”

Section: Introductionmentioning

confidence: 99%

Robustness of the EWMA median control chart to non-normality

Lin

Chou

Chen

2017

IJISE

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Abstract:The control charts with exponentially weighted moving average (EWMA) had been shown to be effective for detecting small shifts in the mean of the process characteristic. When the data depart from normality or have the presence of outliers, the sample median might be used to provide a fairer representation of centrality of the data. In the present paper, the performances of the EWMA median control charts are evaluated under several distributions. The average run length (ARL) is applied to evaluate the performance of control charts, and the method for calculating ARL of the EWMA median chart is developed using the integral equation approach. Based on our study, the EWMA median chart with a small value of smoothing constant has a low false alarm rate. But as the shift of process mean is large, to maintain the detection ability of the chart, the value of smoothing constant should be increased. In addition, if the data follow a heavy-tailed distribution, it can be shown that the EWMA median chart is always more efficient than the EWMA average chart in detecting the shift of process mean.

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Average Run Lengths for Exponentially Weighted Moving Average Control Schemes Using the Markov Chain Approach

Cited by 87 publications

References 2 publications

Robust economic and economic-statistical design of EWMA control chart

Robust economic and economic-statistical design of EWMA control chart

Joint economic design of EWMA control charts for mean and variance

Robustness of the EWMA median control chart to non-normality

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