• 응용통계연구
• /
• 제33권2호
• /
• pp.161-170
• /
• 2020

${\bar{X}}-S^2$ 관리도는 공정 평균과 산포의 변화를 동시에 탐지하는 전통적인 관리도들 중 하나이다. 일반적으로 사용하는 ${\bar{X}}-S^2$ 관리도의 설계 방법은 병행하는 관리도의 오경보율은 주어진 값을 만족하면서 각 관리도는 동일한 개별적인 오경보율을 갖도록 설정하는 것이다. 이 논문에서는 각 관리도의 개별 오경보율을 다르게 설정하고 이것이 ${\bar{X}}-S^2$ 관리도의 성능에 어떠한 영향을 주는지 살펴보았다. 이를 위해 ${\bar{X}}$ 관리도의 오경보율을 S² 관리도의 오경보율에 γ배한 경우를 고려하였고, γ값에 따른 ${\bar{X}}-S^2$ 관리도 성능을 비교하였다. 관리도의 성능을 평가하는 측도로는 특정한 변화에 대한 성능을 판단하는 경우 이상상태에서의 평균런길이를 사용하였고, 전반적인 성능을 판단하는 경우 RMI(relative mean index)를 사용하였다.

• 한국경영과학회지
• /
• 제39권1호
• /
• pp.1-12
• /
• 2014

This article proposes a variable sampling interval (VSI) $\bar{X}$ control chart using weighted standard deviation (WSD) method for skewed populations. The WSD method decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts control limits and warning limits of a control chart in accordance with the direction and degree of skewness. A control chart constant is derived for estimating the standard deviation of skewed distributions with the mean of sample standard deviations. The proposed chart is compared with the conventional VSI $\bar{X}$ control chart under some skewed distributions. Simulation study shows that the proposed WSD VSI chart can control the in-control average time to signal (ATS) as an adequate level better than the conventional VSI chart, and the proposed chart can detect a decrease in the process mean of a quality characteristic following a positively skewed distribution more quickly than the standard VSI chart.

• 품질경영학회지
• /
• 제45권4호
• /
• pp.943-956
• /
• 2017

Purpose: This paper proposes a VSS(Variable Sample Size) ${\bar{X}}$ control chart using surrogate variable and shows its effectiveness compared with FSS(Fixed Sample Size) ${\bar{X}}$ control chart using either performance variable or surrogate variable. Methods: The expected cost function of VSS ${\bar{X}}$ control chart is derived. The optimal designs are then found for numerical examples using a GA(genetic algorithm) and compared to those of the FSS ${\bar{X}}$ control charts. Results: Computational results show that VSS ${\bar{X}}$ control chart using surrogate variables is superior to FSS ${\bar{X}}$ control chart using either performance variable or surrogate variable from the economic view points. Conclusion: The proposed VSS ${\bar{X}}$ control chart will be useful in industry fields where a performance variable is not avaliable or too costly.

• 품질경영학회지
• /
• 제31권2호
• /
• pp.117-130
• /
• 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.

• 품질경영학회지
• /
• 제32권4호
• /
• pp.156-168
• /
• 2004

This research investigates the statistical efficiency of variable sampling size & sampling interval(VSSI) $\bar{X}$ charts under two assignable causes. Algorithms for calculating the average run length(ARL) and average time to signal(ATS) of the VSSI $\bar{X}$ chart are proposed by employing Markov chain method. States of the process are defined according to the process characteristics after the occurrence of an assignable cause. Transition probabilities are carefully derived from the state definition. Statistical properties of the proposed chart are also investigated. A simple procedure for designing the proposed chart is presented based on the properties. Extensive sensitivity analyses show that the VSSI $\bar{X}$ chart is superior to the VSS or VSI $\bar{X}$ chart as well as to the Shewhart $\bar{X}$ chart in statistical sense, even tinder two assignable causes.

• 품질경영학회지
• /
• 제40권3호
• /
• pp.327-336
• /
• 2012

Purpose: In this study, we research the hurdle rate method to suggest the robust control chart for a contaminated process less vulnerable to fault values than existing control charts. Methods: We produce the results of p, ARL values to compare the performance of two control charts, $\bar{x}-s$ that has been used typically and TM-TS that is suggested by this paper. We implement the simulation focusing on three cases, change of deviation, mean and both of them. Results: We draw a conclusion that the TM-TS control chart has better efficiency than $\bar{x}-s$ control chart over the three cases. Conclusion: We insist that applying TM-TS control chart for a polluted process is more effective than $\bar{x}-s$ control chart.

• 품질경영학회지
• /
• 제44권4호
• /
• pp.751-770
• /
• 2016

Purpose: Two-stage ${\bar{X}}$ chart is a useful tool for process control when a surrogate variable may be used together with a performance variable. This paper extends the two-stage ${\bar{X}}$ chart to a three stage version by decomposing the first stage into the preliminary stage and the main stage. Methods: The expected cost function is derived using Markov-chain approach. The optimal designs are found for numerical examples using a genetic algorithm combined with a pattern search algorithm and compared to those of the two-stage ${\bar{X}}$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the two-stage ${\bar{X}}$ chart in terms of the expected cost per unit time unless the correlation between the performance and surrogate variables is modest and the shift in process mean is smallish. Conclusion: Three-stage ${\bar{X}}$ chart may be a useful alternative to the two-stage ${\bar{X}}$ chart especially when the correlation between the performance and surrogate variables is relatively high and the shift in process mean is on the small side.

• 대한안전경영과학회지
• /
• 제14권3호
• /
• pp.167-174
• /
• 2012

In the manufacturing process the most widely used $\bar{X}$ chart has been applied to control the process mean. Also, Accelerated Life Test(ALT) is commonly used for efficient assurance of product life in development phases, which can be applied in production reliability acceptance test. When life data has lognormal distribution, through censored ALT design so that censored ALT data has asymptotic normal distribution, $ALT\bar{X}$ control chart integrating $\bar{X}$ chart and ALT procedure could be applied to control the mean of process in the manufacturing process. In the situation that process variation is controlled, $Z_p$ control chart is an effective method for the very small fraction nonconforming of quality characteristic. A simultaneous control scheme with $ALT\bar{X}$ control chart and $Z_p$ control chart is designed for the very small fraction nonconforming of product lifetime.

• 산업경영시스템학회지
• /
• 제38권1호
• /
• pp.15-20
• /
• 2015

Control charts are generally used for process control, but the role of traditional control charts have been limited in case of a non-contaminated process. Traditional ${\bar{x}}$-s control chart has not been activated well for such a problem because of trying to control processes as center line and control limits changed by the contaminated value. This paper suggests modified ${\bar{x}}$-s control chart based on robust estimation. In this paper, we consider the trimmed mean of the sample means and the trimmed mean of the sample standard deviations. By comparing with ARL value, the responding results are decided. The comparison resultant results of traditional control chart and modified control chart are contrasted.

• 품질경영학회지
• /
• 제28권3호
• /
• pp.18-30
• /
• 2000

Recent studies have shown that the $\bar{X}$ chart with variable sampling intervals(VSI) and the $\bar{X}$ chart with variable sample size(VSS) are much quicker than Shewhart $\bar{X}$ chart in detecting shiks in the process. Shewhart $\bar{X}$ chart has been beneficial to detect large shifts but it is hard to apply Shewhart $\bar{X}$ chart in detecting moderate shifts in the process mean. In this article the $\bar{X}$ chart using variable sample size(VSS) and variable sampling Intervals(VSI) has been proposed to supplement the weak point mentioned above. So the purpose of this paper is to consider finding the design parameters which minimize expected loss costs for unit process time and measure the performance of VSSI(variable sample size and sampling interval) $\bar{X}$ chart. It is important that assignable causes be detected to maintain the process controlled. This paper has been studied under the assumption that one cycle is from starting of the process to eliminating the assignable causes in the process. The other purpose of this article is to represent the expected loss costs in one cycle with three process parameters(sample size, sampling interval and control limits) function and find the three parameters.