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http://dx.doi.org/10.7469/JKSQM.2015.43.4.471

Economic-Statistical Design of Double Sampling T2 Control Chart under Weibull Failure Model  

Hong, Seong-Ok (General Services Division, Statistics Korea)
Lee, Min-Koo (Department of Information & Statistics, Chungnam National University)
Lee, Jooho (Department of Information & Statistics, Chungnam National University)
Publication Information
Journal of Korean Society for Quality Management / v.43, no.4, 2015 , pp. 471-488 More about this Journal
Abstract
Purpose: Double sampling $T^2$ chart is a useful tool for detecting a relatively small shift in process mean when the process is controlled by multiple variables. This paper finds the optimal design of the double sampling $T^2$ chart in both economical and statistical sense under Weibull failure model. Methods: The expected cost function is mathematically derived using recursive equation approach. The optimal designs are found using a genetic algorithm for numerical examples and compared to those of single sampling $T^2$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling $T^2$ chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling $T^2$ chart can be designed to satisfy both economic and statistical requirements under Weibull failure model and the resulting design is better than the single sampling counterpart.
Keywords
$T^2$ Control Chart; Double Sampling; Weibull Failure Model; Economic-Statistical Design;
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