• Journal of Korean Society for Quality Management
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• v.28 no.3
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• pp.18-30
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• 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.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.156-168
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• 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.

• Proceedings of the Korean Society for Quality Management Conference
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• 2004.04a
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• pp.64-69
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• 2004

This research investigates statistical characteristics of variable sampling size & interval(VSSI) X charts under two assignable causes. Algorithms for calculating the average run length(ARL) and average time to signal(ATS) of the VSSI X chart are proposed by employing Markov chain method. Extensive sensitivity analysis shows that the VSSI. X chart is superior to the VSS or VSI X chart as well as to the Shewhart X chart in statistical sense, even under two assignable causes.

• Proceedings of the Korean Society for Quality Management Conference
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• 2004.04a
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• pp.507-512
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• 2004

This research investigates economic-statistical characteristics of variable sampling size & interval(VSSI) X charts under two assignable causes. We propose the procedure for designing VSSI X charts, based on Lorenzen and Vance model. Computational experiments show that the VSSI X chart Is superior to the Shewhart X chart in the economic-statistical sense, even under two assignable causes

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.1
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• pp.87-98
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• 2005

This research investigates economic-statistical characteristics of variable sampling size and interval (VSSI)$\bar{X}$charts under two assignable causes. A Markov chain approach is employed in order to calculate average run length (ARL) and average time to signal (ATS). Six transient states are derived by carefully defining the state. A steady state cost rate function is constructed based on Lorenzen and Vance(1986) model. The cost rate function is optimized with respect to six design parameters for designing the VSSI $\bar{X}$ charts. Computational experiments show that the VSSI $\bar{X}$ chart is superior to the Shewhart $\bar{X}$ chart in the economic-statistical sense, even under two assignable causes. A comparative study shows that the cost rate may increase up to almost 30% by overlooking the second cause. Critical input parameters are also derived from a sensitivity study and a few guideline graphs are provided for determining the design parameters.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1487-1498
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• 2016

In monitoring a process, in-control process parameters must be estimated from the Phase I data. When we design the control chart based on the estimated process parameters, the control limits are usually chosen to satisfy a specific in-control average run length (ARL). However, as the run length distribution is skewed when the process is either in-control or out-of-control, the median run length (MRL) can be used as alternative measure instead of the ARL. In this paper, we evaluate the performance of Shewhart $\bar{X}$ chart with estimated parameters in terms of the average of median run length (AMRL) and the standard deviation of MRL (SDMRL) metrics. In simualtion study, the grand sample mean is used as a process mean estimator, and several competing process standard deviation estimators are used to evaluate the in-control performance for various amounts of Phase I data.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.5
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• pp.422-428
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• 2013

In many cases, an $\bar{X}$ control chart which is based on the performance variable is used in industrial fields. However, if the performance variable is too costly or impossible to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we propose a model for the economic design of a VSI (Variable Sampling Interval) $\bar{X}$ control chart using a surrogate variable that is linearly correlated with the performance variable. The total average profit model is constructed, which involves the profit per cycle time, the cost of sampling and testing, the cost of detecting and eliminating an assignable cause, and the cost associated with production during out-of-control state. The VSI $\bar{X}$ control charts using surrogate variables are expected to be superior to the Shewhart FSI (Fixed Sampling Interval) $\bar{X}$ control charts using surrogate variables with respect to the expected profit per unit cycle time from economic viewpoint.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.52
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• pp.347-354
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• 1999

Statistical Process Control(SPC) which uses control charts is widely used to inspect and improve manufacturing process as a effective method. A parametric method is the most common in statistical process control. Shewhart chart was made under the assumption that measurements are independent and normal distribution. In practice, this assumption is often excluded, for example, in case of (equation omitted) chart, when the subgroup sample is small or correlation, it happens that measured data have bias or rejection of the normality test. A bootstrap method can be used in such a situation, which is calculated by resampling procedure without pre-distribution assumption. In this study, applying bootstrap percentile method to (equation omitted) chart, it is compared and evaluated standard process control limit with bootstrap percentile control limit. Also, under the normal and non-normal distributions, where parameter is 0.5, using computer simulation, it is compared standard parametric with bootstrap method which is used to decide process control limits in process quality.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.487-501
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• 2017

A machine vision system (MVS) is a computer system that utilizes one or more image-capturing devices to provide image data for analysis and interpretation. Recently there have been a number of industrial- and medical-device applications where control charts have been proposed for use with image data. The use of image-based control charting is somewhat different from traditional control charting applications, and these differences can be attributed to several factors, such as the type of data monitored and how the control charts are applied. In this paper, we investigate the adjustment effect of image size and region of interest (ROI) size, when we use control charts to monitor grayscale image data in industry.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.39-56
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• 2000

${\overline{X}}$ control chart has proven to be an effective tool to improve the product quality. Shewhart charts assume that the observations are independent and normally distributed. Under the presence of positive autocorrelation and severe skewness, the control limits are not accurate because assumptions are violated- Autocorrelation in process measurements results in frequent false alarms when standard control chats are applied in process monitoring. In this paper, Threshold Bootstrap and Moving Block Bootstrap are used for constructing a confidence interval of correlated observations. Monte Carlo simulation studies are conducted to compare the performance of the bootstrap methods and that of standard method for constructing control charts under several conditions.