• Journal of Korean Society for Quality Management
• /
• v.33 no.3
• /
• pp.126-134
• /
• 2005

This paper proposes a selectively cumulative sum(S-CUSUM) control chart for detecting shifts in the process mean. The basic idea of the S-CUSUM chart is to accumulate previous samples selectively in order to increase the sensitivity. The S-CUSUM chart employs a threshold limit to determine whether to accumulate previous samples or not. Consecutive samples with control statistics out of the threshold limit are to be accumulated to calculate a standardized control statistic. If the control statistic falls within the threshold limit, only the next sample is to be used. During the whole sampling process, the S-CUSUM chart produces an 'out-of-control' signal either when any control statistic falls outside the control limit or when L -consecutive control statistics fall outside the threshold limit. The number L is a decision variable and is called a 'control length'. A Markov chain approach is employed to describe the S-CUSUM sampling process. Formulae for the steady state probabilities and the Average Run Length(ARL) during an in-control state are derived in closed forms. Some properties useful for designing statistical parameters are also derived and a statistical design procedure for the S-CUSUM chart is proposed. Comparative studies show that the proposed S-CUSUM chart is uniformly superior to the CUSUM chart or the Exponentially Weighted Moving Average(EWMA) chart with respect to the ARL performance.

• Journal of the Korea Society of Computer and Information
• /
• v.25 no.12
• /
• pp.73-82
• /
• 2020

Most process date such as semiconductor and petrochemical processes, autocorrelation often exists between observed data, but when the existing SPC(Statistical process control) is applied to these processes, it is not possible to effectively detect the average change of the process. In this paper, when the average change of a certain size occurs in the process data following a specific time series model, the average of the residuals changes according to the passage of time, and the change pattern of the average is introduced around the ARMA(1,1) process. Based on this result, the reference value required in the design process of the CUSUM (Cumulative sum) control chart is appropriately considered by considering the type of the time series model of the process data of the CUSUM control chart that can detect small mean changes in the process and the width of the process mean change of interest. It was confirmed through simulation that it should be selected and used.

• 한국데이터정보과학회:학술대회논문집
• /
• 2003.05a
• /
• pp.89-95
• /
• 2003

Cumulative sum(CUSUM) control charts for monitoring dispersion matrix under multivariate normal process are proposed. Performances of the proposed CUSUM charts are measured in terms of average run length(ARL) by simulation. Numerical results show that small reference values of the proposed CUSUM chart is more efficient for small shifts in the production process.

• Journal of the Korean Data and Information Science Society
• /
• v.12 no.1
• /
• pp.127-133
• /
• 2001

In this article we establish multivariate cumulative sum (CUSUM) control charts based on residual vector with correlated observations. We first find the residual vector and its expectation and variance-covariance matrix and then evaluate the average run length (ARL) of the control charts.

• Journal of Integrative Natural Science
• /
• v.13 no.4
• /
• pp.152-157
• /
• 2020

To monitor all elements simultaneously of variance-covariance matrix Σ of several correlated quality characteristics under multivariate normal process Np($\underline{\mu}$, Σ), multivariate exponentially weighted moving average (EWMA) chart and cumulative sum (CUSUM) chart are considered and compared. Numerical performances of the considered variable sampling interval (VSI) charts are evaluated using average run length (ARL), average time to signal (ATS), average number of switches (ANSW) to signal, and the probability of switch Pr(switch) between two sampling interval d1 and d2 where d1 < d2. For small or moderate changes of Σ, the performances of multivariate EWMA chart is approximately equivalent to that of multivariate CUSUM chart.

• The Korean Journal of Applied Statistics
• /
• v.34 no.5
• /
• pp.735-744
• /
• 2021

Maintaining the lifetime of a product is one of the objectives of quality control. In real processes, most samples are constructed with censored data because, in many situations, we cannot measure the lifetime of all samples due to time or cost problems. In this paper, we propose two cumulative sum (CUSUM) control charting procedures to monitor the mean of type I right-censored lognormal lifetime data. One of them is based on the likelihood ratio, and the other is based on the binomial distribution. Through simulations, we evaluate the performance of the two proposed procedures by comparing the average run length (ARL). The overall performance of the likelihood ratio CUSUM chart is better, especially this chart performs better when the censoring rate is low and the shape parameter value is small. Conversely, the binomial CUSUM chart is shown to perform better when the censoring rate is high, the shape parameter value is large, and the change in the mean is small.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2006.11a
• /
• pp.560-570
• /
• 2006

This paper proposes a selectively cumulative sum (S-CUSUM) control chart with variable sampling intervals (VSI) for detecting shifts in the process mean. The basic idea of the VSI S-CUSUM chart is to adjust sampling intervals and to accumulate previous samples selectively in order to increase the sensitivity. The VSI S-CUSUM chart employs a threshold limit to determine whether to increase sampling rate as well as to accumulate previous samples or not. If a standardized control statistic falls outside the threshold limit, the next sample is taken with higher sampling rate and is accumulated to calculate the next control statistic. If the control statistic falls within the threshold limit, the next sample is taken with lower sampling rate and only the sample is used to get the control statistic. The VSI S-CUSUM chart produces an 'out-of-control' signal either when any control statistic falls outside the control limit or when L-consecutive control statistics fall outside the threshold limit. The number L is a decision variable and is called a 'control length'. A Markov chain model is employed to describe the VSI S-CUSUM sampling process. Some useful formulae related to the steady state average time-to signal (ATS) for an in-control state and out-of-control state are derived in closed forms. A statistical design procedure for the VSI S-CUSUM chart is proposed. Comparative studies show that the proposed VSI S-CUSUM chart is uniformly superior to the VSI CUSUM chart or to the Exponentially Weighted Moving Average (EWMA) chart with respect to the ATS performance.

• Journal of Korean Society for Quality Management
• /
• v.32 no.4
• /
• 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.

• Management Science and Financial Engineering
• /
• v.6 no.1
• /
• pp.1-19
• /
• 2000

This papeer proposes a general approach of the multivariate expontially weighted moving average(MEWMA) chart, in which the smoothing matrix has full elements instead of only diagonal elements. The average run length (ARL) properties of this scheme are examined for a diverse set of quality control environments and the information to design the chhart is provied. Performance of the scheme is measured by estmating ARL and compared to those of two group cumulative sum (CUSUM) chats. The comparison resullts show that the MEWMA chart can improve its ARL performance in detecting a small shifts out-of-control in the start-up stage, the general MEWMA chart of a full smoothing matrix appears to offer an exceptional protection aginst departures from control in the process mean.

• Journal of Korean Society for Quality Management
• /
• v.34 no.4
• /
• pp.102-109
• /
• 2006

This paper investigates the effects of non-normality on the performance of univariate and multivariate cumulative sum(CUSUM) control charts for monitoring the process mean. In-control and out-of-control average run lengths of the charts are examined for the univariate/multivariate lognormal and t distributions. The effects of the reference value and the correlation coefficient under the non-normal distributions are also studied. Simulation results show that the CUSUM charts with small reference values are robust to non-normality but those with moderate or large reference values are sensitive to non-normal data especially to process data from skewed distributions. The performance of the chart to detect mean shift of a process is not invariant to the direction of the shift for skewed distributions.