• 품질경영학회지
• /
• 제35권1호
• /
• pp.24-34
• /
• 2007

This paper investigates the average run length (ARL) of a selectively moving average (S-MA) control chart. The S-U chart is designed to detect shifts in the process mean. The basic idea of the S-MA chart is to accumulate previous samples selectively in order to increase the sensitivity. The ARL of the S-MA chart was shown to be monotone decreasing with respect to the decision length in a previous research [3]. This paper derives the steady-state ARL in a closed-form and shows that the monotone property is resulted from head-start assumption. The steady-state ARL is shown to be a sum of head-start ARL and an additional term. The statistical design procedure for the S-MA chart is revised according to this result. Sensitivity study shorts that the steady-state ARL performance is still better than the CUSUM chart or the Exponentially Weighted Moving Average (EWMA) chart.

• 산업경영시스템학회지
• /
• 제18권36호
• /
• pp.243-251
• /
• 1995

본 연구에서는 자동상관인 공정의 변화를 빠르게 탐지할 수 있는 Special-Cause CUSUM 관리도를 사용하여 다섯가지 시계열 모델에 대해 다음과 같은 연구를 수행한다. 첫째 ACF와 PACF로 파라미터에 따른 ARL의 변화를 쉽게 해석할 수 있는 방법과 둘째로 독립인 관측값에 적용하는 Hawkins(1992)의 ARL 간략계산법을 자동상관인 공정에서도 사용할 수 있는 기법을 제시하여 기존의 시뮬레이션을 이용한 ARL 계산법에 비해 빠르고도 정확한 값을 구한다. 끝으로 두가지 유형의 평균이동에 대한 ARL 변화를 각각 계산해 보아 그 효과를 비교분석 한다.

• 품질경영학회지
• /
• 제26권3호
• /
• pp.31-45
• /
• 1998

This paper proposes a method of designing one-sided cumulative scored control charts to control the process mean with a normally distributed quality characteristic. The average run length(ARL) is obtained from the average sample number of sequential probability ratio test(SPRT) on trinomial distribution. Using the analogy between cumulative scored control chart and SPRT for trinomial observations, a procedure is presented to determine three control chart parameters; lower and u, pp.r scoring boundaries and action limit. The parameters are determined by minimizing the ARL when the process is out of control with prespecified ARL when the process is in control.

• 응용통계연구
• /
• 제31권4호
• /
• pp.485-495
• /
• 2018

CCC-r 관리도는 고품질공정에서 공정불량률을 관리하는 경우 매우 효율적이라고 알려져 있다. 이 관리도를 사용할 때 관리상태의 공정모수는 일반적으로 알려져 있지 않기 때문에 제1국면의 표본을 추출하여 이를 추정해야 한다. 제2국면에서 관리도의 성능은 제1국면에서 추정한 모수와 관리한계에 영향을 받기 때문에, 추정 오차의 영향을 살펴보는 것은 중요하다. 이 논문에서는 일반적으로 많이 사용하는 평균런길이의 평균(average of average run length) 이외에 평균런길이의 표준편차(standard deviation of average run length)를 사용하여 CCC-r 관리도의 관리상태의 성능을 평가하였다. 그 결과 CCC-r 관리도에서 안정적인 관리상태의 성능을 유지하기 위해서는 이전에 권장하던 제1국면의 표본 크기보다 훨씬 더 큰 표본이 필요하다는 사실을 알 수 있었다.

• Journal of the Korean Statistical Society
• /
• 제23권1호
• /
• pp.89-102
• /
• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• 품질경영학회지
• /
• 제32권4호
• /
• pp.169-183
• /
• 2004

The synthetic control chart (SCC) proposed by Wu and Spedding (2000) is to detect shifts in the process mean. The performance was re-evaluated by Davis and Woodall (2002), and the steady-state average run length (ARL) performance was shown to be inferior to cumulative sum (CUSUM) or exponentially weighted moving average (EWMA) chart This paper proposes a simple adaptive scheme to improve the performance of the synthetic control chart. That is, once a non-conforming (NC) sample occurs, we investigate the next L-consecutive samples with larger sample sizes and shorter sampling intervals. We employ a Markov chain model to derive the ARL and the average time to s19na1 (ATS). We also propose a statistical design procedure for determining decision variables. Comprehensive comparative study shows that the proposed control chart is uniformly superior to the original SCC or double sampling (DS) Χ chart and comparable to the EWMA chart in ATS performance.

• 품질경영학회지
• /
• 제27권4호
• /
• pp.143-152
• /
• 1999

In Shewhart control chart, the average run length(ARL) is calculated using the mean of a conventional geometric distribution(CGD) assuming a sequence of identical and independent Bernoulli trials. In this, the success probability of CGB is the probability that any point exceeds the control limits. When the process is in-control state, there is no problem in the above assumption since the probability that any point exceeds the control limits does not change if the in-control state continues. However, if the out-of-control state begins and continues during the process, the probability of exceeding the control limits may take two forms. First, once the out-of-control state begins with exceeding probability p, it continues with the same exceeding probability p. Second, after the out-of-control state begins, the exceeding probabilities may very according to some pattern. In the first case, ARL is the mean of CGD with success probability p as usual. But in the second case, the assumption of a sequence of identical and independent Bernoulli trials is invalid and we can not use the mean of CGD as ARL. This paper concentrate on that point. By adopting one generalized binomial distribution(GBD) model that allows correlated Bernoulli trials, generalized geometric distribution(GGD) is defined and its mean is derived to find an alternative ARL when the process is in out-of-control state and the exceeding probabilities take the second form mentioned in the above. Small-scale simulation is performed to show how an alternative ARL works.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 추계 학술발표회 논문집
• /
• pp.97-103
• /
• 2003

Shewhart-type control charts have historically been used for attribute data, though they have ARL biased property and even are unable to detect the improvement of a process with some process parameters. So far most efforts have been made to improve the performance of attribute control charts in terms of faster detection of special causes without increasing the rates of false alarm. In this paper, control limits are proposed that yield an ARL (nearly) unbiased chart for attributes. Optimal design is also proposed for attribute control charts under a natural sense of criterion.

• 품질경영학회지
• /
• 제26권2호
• /
• pp.51-60
• /
• 1998

Exponetially weighted moving average(EWMA) control chart to simultaneously monitor correlation coefficients of several correlated quality variables under multivariate normal process are proposed. Performances of the proposed control charts are measured in terms of average run length(ARL) by simulation. Numerical results show that smaller values of smoothing constant are more efficient in terms of ARL.

• Journal of the Korean Data and Information Science Society
• /
• 제13권1호
• /
• pp.105-112
• /
• 2002

In this paper we establish bivariate exponentially weighted moving average (EWMA) control charts for autocorrelated processes using residual vectors. We first derive the residual vectors, their expectation, variance-covariance matrix, then evaluate the control chart based on the average run length (ARL).