scholarly journals Statistical Design of an Adaptive SyntheticX-Control Chart with Run Rule on Service and Management Operation

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Shucheng Yu ◽  
Qiang Wan ◽  
Zhenghong Wei ◽  
Tianbo Tang
Keyword(s):  
Control Chart ◽  
Statistical Design ◽  
Sampling Interval ◽  
Cusum Chart ◽  
Process Mean ◽  
Markov Chain Approach ◽  
Variable Sampling ◽  
Proposed Model ◽  
Adaptive Schemes ◽  
Management Operation

An improved syntheticX-control chart based on hybrid adaptive scheme and run rule scheme is introduced to enhance the statistical performance of traditional syntheticX-control chart on service and management operation. The proposed scientific hybrid adaptive schemes consider both variable sampling interval and variable sample size scheme. The properties of the proposed chart are obtained using Markov chain approach. An extensive set of numerical results is presented to test the effectiveness of the proposed model in detecting small and moderate shifts in the process mean. The results show that the proposed chart is quicker than the standard syntheticX-chart and CUSUM chart in detecting small and moderate shifts in the process of service and management operation.

scholarly journals Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

2016 ◽  
Vol 7 (4) ◽  
pp. 54-64
Author(s):  
Tae-Hoon Lee ◽  
Sung-Hoon Hong ◽  
Hyuck-Moo Kwon ◽  
Minkoo Lee
Keyword(s):  
Genetic Algorithms ◽  
Control Chart ◽  
Statistical Design ◽  
Sampling Interval ◽  
Performance Variable ◽  
Variable Sampling Interval ◽  
Surrogate Variable ◽  
Variable Sampling ◽  
Proposed Model ◽  
A Performance

Abstract In many cases, a $\overline X $ control chart based on a performance variable is used in industrial fields. Typically, the control chart monitors the measurements of a performance variable itself. 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 present a model for the economic statistical design of a VSI (Variable Sampling Interval) $\overline X $ control chart using a surrogate variable that is linearly correlated with the performance variable. We derive the total average profit model from an economic viewpoint and apply the model to a Very High Temperature Reactor (VHTR) nuclear fuel measurement system and derive the optimal result using genetic algorithms. Compared with the control chart based on a performance variable, the proposed model gives a larger expected net income per unit of time in the long-run if the correlation between the performance variable and the surrogate variable is relatively high. The proposed model was confined to the sample mean control chart under the assumption that a single assignable cause occurs according to the Poisson process. However, the model may also be extended to other types of control charts using a single or multiple assignable cause assumptions such as VSS (Variable Sample Size) $\overline X $ control chart, EWMA, CUSUM charts and so on.

scholarly journals Economic and Economic-Statistical Design of Multivariate Bayesian Control Chart with Variable Sampling Intervals

2020 ◽  
pp. 737-750
Author(s):  
Masoud Tavakoli ◽  
Reza Pourtaheri
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Fixed Ratio ◽  
Statistical Design ◽  
Sampling Interval ◽  
Design Parameters ◽  
Variable Sampling ◽  
Sampling Intervals ◽  
Bayesian Control ◽  
T2 Control Chart

Due to the proper performance of Bayesian control chart in detecting process shifts, it recently has become the subject of interest. It has been proved that on Bayesian and traditional control charts, the economic and statistical performances of the variable sampling interval (VSI) scheme are superior to those of the fixed ratio sampling (FRS) strategy in detecting small to moderate shifts. This paper studies the VSI multivariate Bayesian control chart based on economic and economic-statistical designs. Since finding the distribution of Bayesian statistic is t complicated, we apply Monte Carlo method and we employ artificial bee colony (ABC) algorithm to obtain the optimal design parameters (sample size, sampling intervals, warning limit and control limit). In the end, this case study is compared with VSI Hotelling’s T2 control chart and it is shown that this approach is more desirable statistically and economically.

scholarly journals New One-Sided EWMA t Charts without and with Variable Sampling Intervals for Monitoring the Process Mean

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yan Wang ◽  
Xuelong Hu ◽  
Xiaojian Zhou ◽  
Yulong Qiao ◽  
Shu Wu
Keyword(s):  
Moving Average ◽  
Simulation Method ◽  
Sampling Interval ◽  
Vital Role ◽  
Process Mean ◽  
Statistical Process ◽  
Variable Sampling ◽  
Sampling Intervals ◽  
Process Variance ◽  
Weighted Moving Average

In statistical process control (SPC), t charts play a vital role in the monitoring of the process mean, especially when the process variance is unknown. In this paper, two separate upper-sided and lower-sided exponentially weighted moving average (EWMA) t charts are first proposed and the Monte Carlo simulation method is used to obtain their run length (RL) properties. Compared with the traditional one-sided EWMA t charts and several run rules t charts, the proposed charts are proven to have better performance than these competing charts. In addition, by adding the variable sampling interval (VSI) feature to the proposed charts, the new VSI one-sided EWMA t charts are shown to detect different shift sizes in the process more efficient than the chart without VSI feature. Finally, an example of a milk filling process illustrates the use of the charts.

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