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

Title & Authors
Economic-Statistical Design of Double Sampling T2 Control Chart under Weibull Failure Model
Hong, Seong-Ok; Lee, Min-Koo; Lee, Jooho;

Abstract
Purpose: Double sampling $\small{T^2}$ 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 $\small{T^2}$ 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 $\small{T^2}$ chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling $\small{T^2}$ chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling $\small{T^2}$ 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
$\small{T^2}$ Control Chart;Double Sampling;Weibull Failure Model;Economic-Statistical Design;
Language
Korean
Cited by
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