Economic design of a variable sampling rate EWMA chart

Park, Changsoon; Lee, Jaeheon; Kim, Young-il

doi:10.1080/07408170490426116

Cited by 51 publications

(27 citation statements)

References 26 publications

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“…Hence, a shorter sampling interval helps to constrain the quality related costs which increase with shift sizes. We also remark that, in previous research optimal sampling interval is observed to decrease with shift size for an EWMA mean chart (Park et al, 2004), which is in consistence with our results for the EWMA-m/EWMA-v scheme.…”

Section: Numerical Examplessupporting

confidence: 78%

“…The inverse relationship between the optimal sample size and the magnitude of the shift has also been observed in the economic design of X-bar charts (Montgomery, 1980). The results given in Park et al (2004) for EWMA mean charts also reveal a similar pattern. The reduction in sample size can be explained by the fact that large shifts in mean and/or variance can be detected more easily than small shifts, implying a reduced need for a large sample size.…”

Section: Numerical Examplessupporting

confidence: 63%

“…In the literature on control charts employing an EWMA type statistic, several authors have explored the economic design of EWMA control charts to monitor the process mean (Ho and Case, 1994b;Montgomery et al, 1995). Park et al (2004) extended the traditional economic design of an EWMA chart to the case where the sampling interval and sample size may vary depending on the current chart statistic. Tolley and English (2001) studied the economic design of a control scheme combining both EWMA and X-bar charts.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Numerical Examplessupporting

confidence: 78%

Section: Numerical Examplessupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

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Joint economic design of EWMA control charts for mean and variance

Serel

Moskowitz

2008

European Journal of Operational Research

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“…[18] Ho and Case [19] and Torng et al [20] explored the economic optimal design of EWMA control charts to monitor process shifts. Park et al [21] considered the economic design of the variable sampling rate EWMA control charts to determine the optimal parameter such that the expected total cost is minimized. Some authors have considered the production costs based on a quadratic loss function for economical design.…”

Section: Introductionmentioning

confidence: 99%

Considering Taguchi loss function on statistically constrained economic sum of squares exponentially weighted moving average charts

Huang

2013

Journal of Statistical Computation and Simulation

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In this paper, Duncan's cost model combined Taguchi's quadratic loss function is applied to develop the economic-statistical design of the sum of squares exponentially weighted moving average (SS-EWMA) chart. The genetic algorithm is applied to search for the optimal decision variables of SS-EWMA chart such that the expected cost is minimized. Sensitivity analysis reveals that the optimal sample size and sampling interval decrease; optimal smoothing constant and control limit increase as the mean and/or variance increases. Moreover, the combination of optimal parameter levels in orthogonal array experiment plays an important guideline for monitoring the process mean and/or variance.

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“…Designing and evaluating monitoring schemes using the ECU is usually referred to as the economic design of the scheme. The economic design of SPC control charts has been studied, for example, by Jiang and Tsui (2000), Lorenzen and Vance (1986), Montgomery (1980), Park and Reynolds (1999) and Park, Lee, and Kim (2004).…”

Section: Introductionmentioning

confidence: 99%

Economic design of an integrated process control procedure with repeated adjustments and EWMA monitoring

Park

Reynolds

2008

Journal of the Korean Statistical Society

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Statistical process control (SPC) reduces process variability by detecting and eliminating special causes of process variation, while engineering process control (EPC) reduces variability by adjusting the process to keep the quality variable close to target. This article considers an integrated process control (IPC) procedure that simultaneously applies SPC and EPC techniques to reduce the variation of a process.The process model considered is ARIMA(0, 1, 1) when the process is in control. A repeated adjustment EPC scheme is applied by compensating for the predicted deviation from target. It is assumed that a special cause can change the process level, the process variance, the moving average parameter, or the system gain. Two exponentially weighted moving average (EWMA) control charts are applied to the observed deviations to detect special causes. One EWMA chart is for detecting mean shifts, and the other is for detecting variance increases.The effectiveness of the IPC scheme is evaluated using the expected cost per unit time. One major objective of this article is to investigate the effects of the process and cost parameters on the expected cost per unit time. Another major objective is to give practical guidelines for the efficient selection of the chart parameters of the two EWMA control charts.

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Economic design of a variable sampling rate EWMA chart

Cited by 51 publications

References 26 publications

Joint economic design of EWMA control charts for mean and variance

Joint economic design of EWMA control charts for mean and variance

Considering Taguchi loss function on statistically constrained economic sum of squares exponentially weighted moving average charts

Economic design of an integrated process control procedure with repeated adjustments and EWMA monitoring

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