Optimization of design parameters for control charts with multiple assignable causes

Duncan's economic model of Shewhart's original x¯ chart has established its optimal and economic application for processes with the Markovian failure characteristic. As the sample statistics show some indications of process variations, the variable-sampling-interval (VSI) control charts pe...

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Bibliographic Details
Published in:Journal of applied statistics 2006-04, Vol.33 (3), p.279-290
Main Authors: Yu, Fong-jung, Hou, Jiang-liang
Format: Article
Language:English
Subjects:
Control charts
Economic design
Economic models
Markov analysis
Mathematical models
multiple assignable causes
Statistical Process Control (SPC)
Variable Sampling Interval (VSI)
x-super-¯ control charts
x¯ control charts
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Summary:Duncan's economic model of Shewhart's original x¯ chart has established its optimal and economic application for processes with the Markovian failure characteristic. As the sample statistics show some indications of process variations, the variable-sampling-interval (VSI) control charts perform more effectively than the fixed sampling interval (FSI) ones due to a higher frequency in the sampling rate. Regarding the economic design of control charts, most studies have been dedicated to the FSI scheme. In 1998, Bai & Lee considered the production process with a single assignable cause and proposed an economic VSI design for a general x¯ control chart. However, in real cases, there are multiple assignable causes in the production process. Therefore, concerning the operation characteristics of the real industry, this research develops an economic model for the VSI control chart with multiple assignable causes based on stochastic and statistics theory and determines the optimal design parameters of the chart. A numerical example is also provided to demonstrate the effectiveness of the proposed model and the result indicates that VSI performs more effectively than a FSI control chart.
ISSN:0266-4763
1360-0532
DOI:10.1080/02664760500445541