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 Economic Design of EWMA Control Charts with Variable Sampling Intervals for Monitoring the Mean and Standard Deviation under Preventive Maintenance and Taguchi’s Loss Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Li Xue ◽  
Zhen He
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Economic Model ◽  
Preventive Maintenance ◽  
Control Charts ◽  
Loss Functions ◽  
Variable Sampling ◽  
Sampling Intervals ◽  
Optimal Values ◽  
The Mean

The control chart and the maintenance management need to control process quality and reduce out-of-control cost. They are two key tools in the production process; however, they have usually been analyzed separately in the literature. Moreover, the existing studies integrating these two concepts suffer from three significant drawbacks as follows: (1) using control charts with fixed parameters to monitor the process, so that the small and middle shifts are detected slowly; (2) monitoring the mean and standard deviation separately, whereas, in real condition, the mean and standard deviation should be monitored simultaneously; (3) quality loss function is not usually used to design economic model, which leads to a large social quality loss in the monitoring process of control chart. To eliminate these weaknesses, the economic design of the exponential weighted moving average (EWMA) control chart with variable sampling intervals (VSI) for monitoring the mean and standard deviation under preventive maintenance and Taguchi’s loss functions is proposed. The optimal values of the parameters are determined to minimize the loss-per-item in an average cycle process. In addition, a genetic algorithm is used in a numerical example to search for the optimal values of the parameters. According to the sensitivity analysis, the effect of the model parameters on the solution of the economic model is obtained. Finally, the comparison study shows that the VSI EWMA control charts designed by the joint economic model are expected to reduce loss.

Design of a Variable Sampling Interval EWMA Median Control Chart

2019 ◽  
Vol 26 (05) ◽  
pp. 1950021 ◽  
Author(s):  
Kim Phuc Tran ◽  
Philippe Castagliola ◽  
Thi Hien Nguyen ◽  
Anne Cuzol
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Food Production ◽  
Average Run Length ◽  
Moving Average ◽  
Sampling Interval ◽  
Performance Comparison ◽  
Variable Sampling Interval ◽  
Variable Sampling ◽  
Weighted Moving Average

In the literature, median type control charts have been widely investigated as easy and efficient means to monitor the process mean when observations are from a normal distribution. In this work, a Variable Sampling Interval (VSI) Exponentially Weighted Moving Average (EWMA) median control chart is proposed and studied. The Markov chains are used to calculate the average run length to signal (ARL). A performance comparison with the original EWMA median control chart is made. The numerical results show that the proposed chart is considerably more effective as it is faster in detecting process shifts. Finally, the implementation of the proposed chart is illustrated with an example in food production process.

Comparison Between the Economic-Statistical Design of Double and Triple Sampling X ¯ \bar{X} Control Charts

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Azamsadat Iziy ◽  
Bahram Sadeghpour Gildeh ◽  
Ehsan Monabbati
Keyword(s):  
Optimal Control ◽  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Statistical Design ◽  
Sampling Interval ◽  
Point Of View ◽  
Double Sampling ◽  
Control Limits

AbstractControl charts have been established as major tools for quality control and improvement in industry. Therefore, it is always required to consider an appropriate design of a control chart from an economical point of view before using the chart. The economic design of a control chart refers to the determination of three optimal control chart parameters: sample size, the sampling interval, and the control limits coefficient. In this article, the double sampling (DS)

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.

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