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

Comparison Between the Economic-Statistical Design of Double and Triple Sampling... 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) X¯{\bar{X}}control chart is considered for theeconomic design using nonlinear mixed integer programming approach. The triple sampling (TS) X¯{\bar{X}}control charts are developed for economic design based on the results of solving the DS X¯{\bar{X}}chart design problems.In this model, we assume that the process must be shut down during the search for the assignable cause.Multiple sampling X¯{\bar{X}}charts can be designed for quick detection of a small shift in process.The results of the comparison between the economic-statistical design of DS and TS X¯{\bar{X}}control charts show that TS X¯{\bar{X}}control charts are more efficient in terms of minimizing the average sample size, but its expected average cost takes larger values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

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

, Volume 32 (1): 13 – Jun 1, 2017
13 pages

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Publisher
de Gruyter
© 2017 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6147
eISSN
2367-2404
DOI
10.1515/eqc-2017-0005
Publisher site
See Article on Publisher Site

### Abstract

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) X¯{\bar{X}}control chart is considered for theeconomic design using nonlinear mixed integer programming approach. The triple sampling (TS) X¯{\bar{X}}control charts are developed for economic design based on the results of solving the DS X¯{\bar{X}}chart design problems.In this model, we assume that the process must be shut down during the search for the assignable cause.Multiple sampling X¯{\bar{X}}charts can be designed for quick detection of a small shift in process.The results of the comparison between the economic-statistical design of DS and TS X¯{\bar{X}}control charts show that TS X¯{\bar{X}}control charts are more efficient in terms of minimizing the average sample size, but its expected average cost takes larger values.

### Journal

Economic Quality Controlde Gruyter

Published: Jun 1, 2017

### References

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