• Journal of Korean Society for Quality Management
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• v.20 no.1
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• pp.1-10
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• 1992

When we compare different control charting schemes, the average run length of each control chart is usually used. The use of the average run length implies that there is unbounded number of samples or observations. The regression recursive residuals, however, have been applied to the cumulative sum chart to detect whether the mean or variance changes. To implement choice of decision interval, we calculate the probability that certain fixed number of control statistics stay in the in-control state. This probability can be used as the significance level of a test for detecting the change in the residual mean or variance of the data with a finite number of observations.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.465-470
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• 2012

EWMA(exponentially weighted moving average) charts and CUSUM(cumulative sum) charts are very effective to detect small shifts in the process mean. These charts have some control-chart parameters that allow the charts and be tuned and be more sensitive to certain shifts. The EWMA chart requires users to specify the value of a smoothing parameter, which can also be designed for the size of the mean shift. However, the size of the mean shift that occurs in applications is usually unknown and EWMA charts can perform poorly when the actual size of the mean shift is significantly different from the assumed size. In this paper, we propose the design procedure to find the optimal smoothing parameter of the EWMA chart when the size of the mean shift is unknown.

• Journal of Korean Society for Quality Management
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• v.43 no.4
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• pp.521-532
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• 2015

Purpose: The purpose of this study is to compare two multivariate cumulative sum (MCUSUM) charts designed for spatio-temporal surveillance in terms of not only temporal detection performance but also spatial detection performance. Method: Experiments under various configurations are designed and performed to test two CUSUM charts, namely SMCUSUM and RMCUSUM. In addition to average run length(ARL), two measures of spatial identification accuracy are reported and compared. Results: The RMCUSUM chart provides higher level of spatial identification accuracy while two charts show comparable performance in terms of ARL. Conclusion: The RMCUSUM chart has more flexibility, robustness, and spatial identification accuracy when compared to those of the SMCUSUM chart. We recommend to use the RMCUSUM chart if control limit calibration is not an urgent task.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.11-14
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• 1996

Performance of the group cumulative sum(CUSUM) control scheme using multiple univariate CUSUM charts is more sensitive to the change of quality control(QC) characteristics than the control chart scheme based on the Hotelling statistics. We examine three group charts for multivariate normal data sets simulated with various correlation structures and shift directions in the mean vector. These group schemes apply the orginal measurement vectors, the scaled residual vectors from the regression of each variable on all others and the principal component vectors respectively to calculating the CUSUM statistics. They are also compared to the multivariate QC charts based on the Hotelling statistic by estimating average run lengths, coefficients of variation of run length and ranks in signaling order. On the basis of simulation results, we suggest a control chart scheme appropriate for specific quality control environment.

• Management Science and Financial Engineering
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• v.5 no.1
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• pp.51-71
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• 1999

Performance of the group cumulative sum (CUSUM) control scheme using multiple univariate CUSUM charts is more sensitive to the change of quality control (QC) characteristics than the control chart schemes based on the Hotelling statistic We vexamine three group charts for multivariate normal data sets simulated with various correlation structures and shift directions in the mean vector. These group schemes apply the original measurement vectors, the scaled residual vectors from the re-gression of each variable on all others and the principal component vectors respectively to calculat-ing the CUSUM statistics. They are also compared to the multivariate QC charts based on the Ho-telling statistic by estimating average run lengths, coefficients of variation of run length and ranks in signaling order. On the basis of simulation results, we suggest a control chart scheme appropriate for specific quality control environment.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.4
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• pp.457-468
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• 2007

This paper proposes an adaptive moving average (A-MA) control chart with variable sampling intervals (VSI) for detecting shifts in the process mean. The basic idea of the VSI A-MA chart is to adjust sampling intervals as well as to accumulate previous samples selectively in order to increase the sensitivity. The VSI A-MA chart employs a threshold limit to determine whether or not to increase sampling rate as well as to accumulate previous samples. 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 A-MA 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 control length L is introduced to prevent small mean shifts from being undetected for a long period. A Markov chain model is employed to investigate the VSI A-MA sampling process. 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 A-MA chart is proposed. Comparative studies show that the proposed VSI A-MA chart is uniformly superior to the adaptive Cumulative sum (CUSUM) chart and to the Exponentially Weighted Moving Average (EWMA) chart, and is comparable to the variable sampling size (VSS) VSI EWMA chart with respect to the ATS performance.

• Journal of Digital Convergence
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• v.12 no.6
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• pp.155-160
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• 2014

When we collect marketing data, we can only obtain the bimonthly or quarterly data but the monthly data be available. If we evaluate or predict monthly market condition or establish monthly marketing strategies, we need to disaggregate these bimonthly or quarterly data to the monthly data. In this paper, for bimonthly or quarterly data, we introduce some methods of disaggregation to monthly data. These disaggregation methods include the simple average method, the growth rate method, the weighting method by the judgment of experts, and variable decomposition method using 12 month moving cumulative sum. In this paper, we applied variable decomposition method to disaggregate for bimonthly data of sum of electronics sales in a European country. We, also, introduce how to use this method to predict the future data.

• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.823-833
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• 2016

The lifetime is a key characteristic of product quality. It is best to obtain the lifetime data of all samples, but they are often censored due to time or expense limitations. In this paper, we propose a binomial cumulative sum (CUSUM) chart to monitor the mean of type I right-censored Weibull lifetime data, for a xed value of the Weibull shape parameter. We compare the performance of the proposed binomial CUSUM chart with CUSUM charts studied previously using the steady-state average run length (ARL). The results show that the performance of the binomial CUSUM chart is better when the censoring rate is high and/or the sample size is small.

• Journal of the Korean Society of Clothing and Textiles
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• v.28 no.7
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• pp.983-994
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• 2004

The aim of this study is to provide fundamental data on the development of ready-to-wear clothes appropriate for the body types of elderly women. The study was conducted targeting 318 elderly women over 60 years of age whose fields of action were colleges for the elderly, sports centers, or business sites in Seoul and the neighboring districts. A total of 44 features in the upper body were used for the anthropometric measurement and analysis using anthropometry and photometry. The results of the study are as follows: 1. Somatotypes were classified into three types according to a cluster analysis using height and weight indices. Type 1 is the group with long and undersized upper body and straight body type since the face of the upper body is long relative to height and width, girth and depth are the smallest relative to weight, the breasts are somewhat fat, with a small extent of drooping and a straight back. Type 2 is the group that is considered fat relative to the body, has broad shoulders, drooping breasts with a wide space between them, and a back-bent upper body. Type 3 is the group that has a bent shape, the shortest upper body relative to height, and showing average obesity factors. 2. Indices of height and weight were used for factor analysis, cluster analysis, and discriminant analysis in order to classify upper body somatotype according to shape while excluding size factors of elderly women＇s upper body somatotype. The same method was used to compare and verify the result according to the absolute measurement and height index. Classification based on height and weight indices demonstrate that such somatotype classification minimizes the personal equation of body shape and it induces better classification based on shape as the results showed the highest cumulative sum of square(CUSUM) at 78.38% while six factors showed the smallest result and the hit rate for the classified three groups showed the highest result at 95.30%.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.203-212
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• 2018

Quality requirements of manufactured products or parts are given in the form of specification limits on the quality characteristics of individual units. If a product is to meet the customer's fitness for use criteria, it should be produced by a process which is stable or repeatable. In other words, it must be capable of operating with little variability around the target value or nominal value of the product's quality characteristic. In order to maintain and improve product quality, we need to apply statistical process control techniques such as histogram, check sheet, Pareto chart, cause and effect diagram, or control charts. Among those techniques, the most important one is control charting. The cumulative sum (CUSUM) control charts have been used in statistical process control (SPC) in industries for monitoring process shifts and supporting online measurement. The objective of this research is to apply Taguchi's quality loss function concept to cost based CUSUM control chart design. In this study, a modified quality loss function was developed to reflect quality loss situation where general quadratic loss curve is not appropriate. This research also provided a methodology for the design of CUSUM charts using Taguchi quality loss function concept based on the minimum cost per hour criterion. The new model differs from previous models in that the model assumes that quality loss is incurred even in the incontrol period. This model was compared with other cost based CUSUM models by Wu and Goel, According to numerical sensitivity analysis, the proposed model results in longer average run length in in-control period compared to the other two models.