• Journal of the Korean Data and Information Science Society
• /
• 제23권4호
• /
• pp.807-814
• /
• 2012

We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.

• 품질경영학회지
• /
• 제22권1호
• /
• pp.54-65
• /
• 1994

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. Two basic approaches, "combine-accumulate" approach and "accumulate-combine" approach, for using past sample information in the developement of multivariate EWMA control charts are considered. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average run length (ARL) performances. The numerical results show that multivariate EWMA control charts based on the accumulate-combine approach are more efficient than corresponding multivariate EWMA control charts based on the combine-accumulate approach.

• 대한안전경영과학회지
• /
• 제12권4호
• /
• pp.255-263
• /
• 2010

The research developes short-run standardized control charts(SSCC) and short-run acceptance control charts(SACC) under the various demand patterns. The demand patterns considered in this paper are three types such as high-variety and repetitive low-volume pattern, extremely-high-variety and nonrepetitive low-volume pattern, and high-variety and extremely-low-volume pattern. The short-run standardized control charts developed by extending the long-run ${\bar{x}}$-R, ${\bar{x}}$-s and I-MR charts have strengths for practioners to understand and use easily. Moreover, the short-range acceptance control charts developed in the study can be efficiently used through combining the functions of the inspection and control chart. The weighting schemes such as Shewhart, moving average (MA) and exponentially weighted moving average (EWMA) can be considered by the reliability of data sets. The two types according to the use of control chart are presented in the short-range standardized charts and acceptance control charts. Finally, process capability index(PCI) and process performance index(PPI) classified by the demand patterns are presented.

• Journal of the Korean Data and Information Science Society
• /
• 제4권
• /
• pp.31-44
• /
• 1993

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. A variable sampling interval (VSI) feature is considered in these charts. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average time to signal (ATS) performances. The numerical results show that multivariate VSI EWMA control charts are more efficient than corrsponding multivariate fixed sampling interval (FSI) EWMA control charts.

• Journal of the Korean Data and Information Science Society
• /
• 제20권4호
• /
• pp.741-747
• /
• 2009

Properties of multivariate Shewhart and EWMA (Exponentially Weighted Moving Average) control charts for monitoring variance-covariance matrix of quality variables are investigated. Performances of the proposed charts are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) charts in terms of average time to signal (ATS) and average number of samples to signal (ANSS). Average number of swiches (ANSW) of the proposed VSI charts are also investigated.

• 품질경영학회지
• /
• 제22권4호
• /
• pp.13-27
• /
• 1994

This study is concerned with design of EWMA control charts for counted data. Control charts for the fraction defective and the number of defects are designed. Performance analysis is accomplished for validity of the designed EWMA control charts. Average run length(ARL) is adopted as a criterion for comparison. Simulation results show that the designed EWMA control charts have shorter ARL than pn, p and c control charts when the fraction nonconforming or the average defect number are shifted. This means that the designed control charts can detect the out of -control state of the process more fastly than the traditional control charts.

• 대한안전경영과학회지
• /
• 제12권3호
• /
• pp.257-262
• /
• 2010

The study investigates the various Acceptance Control Charts (ACCs) based on the factors that include process independence, data weighting scheme, subgrouping, and use of control charts. USL - LSL > $6{\sigma}$ that used in the good condition processes in the ACCs are designed by considering user's perspective, producer's perspective and both perspectives. ACCs developed from the research is efficiently applied by using the simple control limit unified with APL (Acceptable Process Level), RLP (Rejectable Process Level), Type I Error $\alpha$, and Type II Error $\beta$. Sampling interval of subgroup examines i.i.d. (Identically and Independent Distributed) or auto-correlated processes. Three types of weight schemes according to the reliability of data include Shewhart, Moving Average(MA) and Exponentially Weighted Moving Average (EWMA) which are considered when designing ACCs. Two types of control charts by the purpose of improvement are also presented. Overall, $\alpha$, $\beta$ and APL for nonconforming proportion and RPL of claim proportion can be designed by practioners who emphasize productivity and claim defense cost.

• International Journal of Quality Innovation
• /
• 제2권1호
• /
• pp.69-86
• /
• 2001

The economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. An MA control chart is more effective than the Shewhart chart in detecting small process shifts [9]. This paper provides an economic model for determining the optimal parameters of an MA control chart with multiple assignable causes and two failures in the production process. These parameters consist of the sample size, the spread of the control limit and the sampling interval. A numerical example is shown and the sensitivity analysis shows that the magnitude of shift, rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost, meaning that one should more carefully estimate these values when conducting an economic analysis.

• 응용통계연구
• /
• 제37권2호
• /
• pp.177-189
• /
• 2024

관리도에서 런길이는 관리 통계량이 관리한계를 벗어날 때까지 관측한 표본의 수로 정의한다. 일반적으로 런길이의 분포는 비대칭이 심하고 변동성이 크기 때문에 평균 런길이만 사용하여 관리도를 설계하고 성능을 평가하는 것은 적절하지 않을 수도 있다. 평균 런길이 기반 설계에 대한 대안으로 이 논문에서는 백분위수를 기반으로 한 관리도의 설계를 소개하고, 이를 지수가중이동평균 관리도의 설계에 적용하는 절차를 제안하고 있다. 이 절차는 백분위수 모수들이 주어진 경우, 모의실험을 통하여 적합된 함수를 사용하여 관리한계의 계수를 설정하는 것이다. 또한 모의실험을 수행하여 제안된 설계 절차를 평균 런길이 기반 설계와 비교하고 평가하였다. 모의실험 결과, 제안된 절차는 이상상태에서 탐지 능력은 거의 유지하면서 관리상태에서의 성능을 향상시킨다는 사실을 확인할 수 있었다.

• 산업경영시스템학회지
• /
• 제35권3호
• /
• pp.52-61
• /
• 2012

The design method for cumulative sum (CUSUM) control charts, which can be robust to autoregressive moving average (ARMA) modeling errors, has not been frequently proposed so far. This is because the CUSUM statistic involves a maximum function, which is intractable in mathematical derivations, and thus any modification on the statistic can not be favorably made. We propose residual-based robust CUSUM control charts for monitoring autocorrelated processes. In order to incorporate the effects of ARMA modeling errors into the design method, we modify parameters (reference value and decision interval) of CUSUM control charts using the approximate expected variance of residuals generated in model uncertainty, rather than directly modify the form of the CUSUM statistic. The expected variance of residuals is derived using a second-order Taylor approximation and the general form is represented using the order of ARMA models with the sample size for ARMA modeling. Based on the Monte carlo simulation, we demonstrate that the proposed method can be effectively used for statistical process control (SPC) charts, which are robust to ARMA modeling errors.