• Proceedings of the Korean Society for Quality Management Conference
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• 2010.04a
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• pp.123-128
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• 2010

This article investigates economic-statistical design of VSI(variable samling interval) charts considering Various Runs Rules. Most recent adaptive control charts are conplex designs. Actually It's not easy to operating control quality process. We propose a procedure for designing VSI Runs charts, based on Lorenzen and Vence's model. The optimal design parameters of the charts can be determined by minimizing the cost model. And computational experiments show that the VSI Runs Rules charts is superior to the FSSI Runs Rules charts in the economic-statistical characterisitics.

• Journal of Korean Society for Quality Management
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• v.32 no.1
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• pp.92-101
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• 2004

Tris paper present an economic statistical design which have statistically constraints for the optimal design of an EWMA control charts with variable sampling interval. Cost function use that proposed by Lorenzen and Vance, and the optimal design parameters include the sample size, control limit width, sampling interval, EWMA weight value. Comparisons between VSI EWMA control charts optimal economic design and optimal economic statistical designs show the following fact. Although have demerits which are more costly than economic design, have merits which to detect shifts more efficiently and to improve statistical performance.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.50
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• pp.55-63
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• 1999

Past studies on economic control charts for controlling process means assumed that the measures of a quality characteristic do not have measurement error. In practice, however, this assumption is frequently violated. In this paper, the economic design models of three control charts(Xbar control chart, Xbar control chart with warning limits, and CUSUM control chart) for controlling process means are developed on the assumption that the measures can have measurement error. The effects of measurement error on the process control cost and design parameters of three economic control charts are examined. According to the experiments done in this study, when measurement error exists, the economic CUSUM control chart has lower process control cost in comparison with two other control charts. When measurement error becomes larger, both the sample size and the sampling interval increase while the control limits decrease.

• International Journal of Quality Innovation
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• v.3 no.2
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• pp.46-56
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• 2002

The presence of imprecise measurement may seriously affect the efficiency of process control and production cost. A cost model is derived to determine the design parameters of the economic asymmetric $\bar{X}$ and S control charts including measurement errors. The effects of imprecise measurement on the performance of the economic asymmetric $\bar{X}$ and S control charts and production cost are examined for the case where the process mean and process standard deviation may change. Application of the proposed control charts is demonstrated through an example. Numerical examples illustrate the effects of imprecise measurement on the design parameters of the proposed control charts. It shows that the imprecision measurement may seriously affrct the ability of the proposed control charts to detect process disturbances quickly, change the sampling frequency, and increase the production cost compared to the control charts excluding measurement errors.

• Journal of Korean Society for Quality Management
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• v.40 no.2
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• pp.186-198
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• 2012

Since Duncan(1956) first proposed an economic design of $\bar{X}$-control charts, most of the succeeding works on economic design of control charts assumed the exponential failure model like Duncan. Hu(1984), however, assumed a more versatile Weibull failure model to develop an economic design of $\bar{X}$-control charts and Banerjee and Rahim(1988) further improved Hu's design by changing the assumption of fixed-length sampling intervals to variable-length ones. In this article we follow the approach of Banerjee and Rahim(1988) but include a pair of warning limits inside the control limits in order to search for a failure without stopping the process when the sample mean falls between warning and control limits. The computational results indicate that the proposed model gives a lower cost than Banerjee and Rahim's model unless the early failure probability of a Weibull distribution is relatively large. The reduction in cost is shown to become larger as the cost of production loss outweighs the cost of searches for a failure.

• Journal of Korean Society for Quality Management
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• v.30 no.2
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• pp.99-117
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• 2002

Variable sampling interval(VSI) and variable sample size(VSS) control charts vary the sampling rate for the next sample depending on the current chart statistic. This paper develops EWMA charts with the VSI and VSS features, and investigates the effectiveness of these charts in context of an economic model. The economic properties of these charts are evaluated by using Markov chain methods. The model contains cost parameters which allow the specification of the costs associated with sampling, false alarms, and operating off target. This economic model can be used to quantify the cost saving that can be obtained by using control charts with the VSI and VSS features instead of with the fixed sampling rate(FSR) feature, and can also be used to gain insight into the way that control charts with the VSI and VSS features should be designed to achieve optimal economic performance. The economic performance of X charts with the VSI and VSS features is also considered.

• International Journal of Quality Innovation
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• v.7 no.3
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• pp.107-115
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• 2006

Control charts are important tools of statistical quality control. In 1956, Duncan first proposed the economic design of $\bar{x}-control$ charts to control normal process means and insure that the economic design control chart actually has a lower cost, compared with a Shewhart control chart. An moving average (MA) control chart is more effective than a Shewhart control chart in detecting small process shifts and is considered by some to be simpler to implement than the CUSUM. An economic design of MA control chart has also been proposed in 2005. The weaknesses to only the economic design are poor statistics because it dose not consider type I or type II errors and average time to signal when selecting design parameters for control chart. This paper provides a construction of an economic-statistical model to determine the optimal parameters of an MA control chart to improve economic design. A numerical example is employed to demonstrate the model's working and its sensitivity analysis is also provided.

• Journal of Korean Society for Quality Management
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• v.24 no.3
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• pp.65-76
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• 1996

This paper is concerned with designing $\bar{X}$-control charts when an estimate error may be Inevitable. Estimate error offen can not be avoided in estimating or measuring the parameter values of the cost model for the control charts. The bounded interval is a common practice to compensate for inherent estimating error. We introduce the 'propagation of error technique to deal with the economic design of the $\bar{X}$-control charts with imprecise information on the cost model parameters. A numerical example is presented to show· its ability in the economic design of $\bar{X}$-control charts.

• Journal of Korean Society for Quality Management
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• v.18 no.1
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• pp.77-83
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• 1990

A model for the economic design of an pn control charts with an assignale cause is presented and the loss-cost function for control schemes using these charts is derived. By minimizing this function with respect to the three control variables, namely, the sample size, the sampling interval and acceptance number, the economically optimal control plan can be optained. The article shows what influence increasing or decreasing condition, according to changeability of the size of these factors, of expected cost can have on the economy when an attribute control chart is used.

• Journal of Korean Society for Quality Management
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• v.31 no.2
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• pp.117-130
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• 2003

This paper investigates the economic design of synthetic control charts. The synthetic control chart has been proven to be statistically superior to the $\bar{X}$-control chart, but its economic characteristics have not been known. We develop an economic model of the synthetic control chart, based on Duncan's model. The synthetic chart has one more decision variable, the lower control limit for the conforming run length. In addition to this, the significance level and the power of the synthetic chart are more complicated than those of the $\bar{X}$-chart. These features make the optimization problem more difficult. We propose an optimization algorithm by adapting the congruent gradient algorithm. We compare the optimal cost of the synthetic chart with that of (equation omitted)-control chart, under the same input parameter set of Duncan’s. For all cases investigated, the synthetic chart shows superior to the $\bar{X}$-chart. The synthetic control chart is easy to implement, and it has better characteristics than the $\bar{X}$-chart in economical sense as well as in statistical sense, so it will be a good alternative to the traditional control charts.