• Journal of Korean Institute of Industrial Engineers
• /
• v.39 no.5
• /
• pp.422-428
• /
• 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 for Quality Management
• /
• v.19 no.2
• /
• pp.172-180
• /
• 1991

The null hypothesis being tested by $the{\bar{X}}$ control chart is that the process is in control at a quality level ${\mu}o$. An ${\bar{X}}control$ chart is a tool for detecting process average changes due to assingnable causes. The major weakness of $the{\bar{X}}$ control chart is that it is relatively insensitive to small changes in the population mean. This paper presents one way to remedy this weakness is to allow each plotted value to depend not only on the most recent subgroup average but on some of the other subgroup averages as well. Two approaches for doing this are based on (1) moving averages and (2) exponentially weighted moving averages of forecasting method.

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

• Proceedings of the Society of Korea Industrial and System Engineering Conference
• /
• 2002.05a
• /
• pp.365-370
• /
• 2002

In this study, according to MARMA(1,0) model which was suggested by Seppala, in case of existing autocorrelation in X control chart and EWMA control chart, the standard method and the non-parametric bootstrap method were compared and analysed using the bootstrap method which use the resampling prediction residual.

• Journal of Korean Society for Quality Management
• /
• v.11 no.1
• /
• pp.44-50
• /
• 1983

The main factors of determining the Control Line of the Control Chart can be classified as follows: 1) sample size (n), 2) the factor that determines the spread of Control Limits (B), (3) sampling frequency (h). The determination of these factors can be explained according to the extent that occurrences of assignable cause should be detected. The purpose of this paper are two: one is for composing a model of which use should be designated for economic decision on the size of these factors leading to the Control Line of the Control Chart, the other is about what influence increasing or decreasing condition, according to changeability of the size of these factors, of expect cost can have on the economy when the Control Chart is used.

• Journal of Korean Society for Quality Management
• /
• v.37 no.2
• /
• pp.46-57
• /
• 2009

The traditional approach to economic design of control charts is based on the assumption that a process is monitored using a performance variable. However, various types of automatic test equipments recently introduced as a part of factory automation usually measure surrogate variables instead of performance variables that are costly to measure. In this article we propose a model for economic design of a control chart which uses a surrogate variable that is highly correlated with the performance variable. The optimum values of the design parameters are determined by maximizing the total average income per cycle time. Numerical studies are performed to compare the proposed $\bar{X}$ control charts with the traditional model using the examples in Panagos et al. (1985).

• Journal of the Korean Data and Information Science Society
• /
• v.27 no.6
• /
• pp.1487-1498
• /
• 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 Society of Industrial and Systems Engineering
• /
• v.22 no.52
• /
• pp.347-354
• /
• 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.

• Journal of Korean Society for Quality Management
• /
• v.40 no.4
• /
• pp.467-480
• /
• 2012

Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical $\bar{X}$ control chart for detecting small process shifts. Methods: The proposed runs rules are compared with other competitive runs rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control ARL at a specified shift of process mean for determining action and warning limits at a time is formulated and a procedure to find two limits is illustrated with a numerical example. Results: The proposed 2-of-3 main and supplementary runs rules demonstrate an improved performance over other runs rules in detecting a sudden shift of process mean by simultaneous changes of mean and standard deviation. Conclusion: To increase the performance in the detection of small to moderate shifts, the proposed runs rules will be used with $\bar{X}$ control charts.

• Food Science and Biotechnology
• /
• v.18 no.3
• /
• pp.745-748
• /
• 2009

Sensory quality variations of jajang sauce were monitored by the $\bar{X}-chart$ and capability analysis based on specifications of each sensory attributes. For sensory quality control (QC) of the sauce which has a strong sweetness and sourness, the ratio of sourness/sweetness was examined as a necessary QC factor to maintain the balance of sweetness and sourness. For the sensory QC factors, all the sensory data were divided into individual sensory score of reference which was a pack of sauce manufactured a week ago. The ratio form of sensory data was useful for decreasing individual variations and for increasing normality of data measured by category scale. The overall proportion of out-spec products under normal manufacturing conditions was obtained by capability analysis of sensory data with normal distribution. Out-spec samples were monitored by the $\bar{X}-chart$ of each sensory attributes.