• 한국경영과학회지
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• 제30권4호
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• pp.1-14
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• 2005

We propose a VSSI-CRL(Variable Sampling Size and Samplina Interval-Conforming Run length) synthetic control chart in order to improve the statistical characteristics of both the VSSI chart and the CRL synthetic chart. The VSSI-CRL chart utilizes VSSI sampling scheme, but it produces a signal only when the CRI is less than a given limit. An algorithm for calculating the ARL(Average Run length) and ATS(Average Time to Signal) of the VSSI-CRL chart is developed by employing Markov chain method. We present some lemmas for describing the statistical characteristics of the VSSI-CRL chart under in-control state. A procedure for designing the VSSI-CRL chart is proposed based on the lemmas. Extensive comparative studios show that the VSSI-CRL chart is superior to the CRL synthetic chart or the VSSI chart in general, and is comparable to the EWMA chart in ATS performance.

• 품질경영학회지
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• 제33권1호
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• pp.1-10
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• 2005

This paper develops a new VSI $\={X}-CRL$ synthetic control chart that considers convenience of use in the field, and perception of change of process applying VSI techniques to synthetic control chart, simultaneously. We found the optimal sampling interval and various control limit factor of the suggested chart using markov chain. Comparison and analysis is carried out between synthetic VSI $\={X}-CRL$ chart and other chart in the statistical aspect; $\={X}$ control chart, VSI $\={X}$ chart, another synthetic chart. In case that the process follows normal distribution, the proposed VSI $\={X}-CRL$ synthetic control chart in detecting process mean shift showed the best performance in aspect of statistical performance, regardless of control limit L of CRL/S control chart.

• 산업경영시스템학회지
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• 제28권4호
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• pp.85-93
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• 2005

This paper is designed a VSI ${\overline{X}}$-CRL synthetic control chart in aspect of economy. We found the optimal sampling interval and various control limit factors under various cost parameters using cost function, proposed Lorenzen and Vance. Optimal design parameters include the sample size, control limit width, sampling interval, CRL/S chart control limit; L. Comparison and analysis of cost parameters are applied between synthetic VSI ${\overline{X}}$-CRL chart and FSI ${\overline{X}}$-CRL chart. The result of this paper shows that VSI ${\overline{X}}$-CRL chart brings cost-cutting effect of 3.04% control expense less than FSI control chart. It may not be difficult to establish the optimal economic control parameters to apply the practical cost parameters in the field.

• 한국산업정보학회논문지
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• 제7권4호
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• pp.53-58
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• 2002

이 논문에서 개별 관측치를 이용한 Shewhart 관리도와 CRL 관리도로 이루어지는 수정된 합성 관리도를 구성한다. Shewhart X 관리도를 적용하여 관리한계선을 벗어나지 않으면 CRL 관리도를 적용하여 한 번 더 공정의 이상유무를 판단하는 2중 감지 공정관리기법을 고려한다. 합성 관리도에서 공정변화를 지적하는 감지력으로 평균 런의 길이()를 이용한다. 논문에서 제안된 수정된 합성 관리도는 We와 Spedding(2000a)이 제안한 합성 관리도와 Shewhart X 관리도보다 우수하며, EWM 관리도와는 성능면에서 매우 유사하다. 또한 공정변화가 0.75$\sigma$보다 클 때는 수정된 합성 관리도가 우수하다는 것을 확인할수 있다. 제시된 X-CRL 관리도를 평가하기 위해 조건부 확률을 계산하여 기존의 관리도와 비교한다.

• 품질경영학회지
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• 제31권2호
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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.