Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions |
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Authors: | Guoliang Tian Kaitai Fang |
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Institution: | (1) Institute of Applied Mathematics, Chinese Academy of Sciences, 100080 Beijing, China;(2) Hong Kong Baptist University, Hong Kong and Institute of Applied Mathematics, Chinese Academy of Sciences, 100080 Beijing, China |
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Abstract: | With order statistics of the uniform distribution on 0, l], exponential and beta distributions, a stochastic representation
is obtained for the uniform distribution over various domains, where A-type domains are closely associated with reliability
growth analysis, order restricted statistical inference and isotonic regression theory, V-type domains are connected with
the mixture-amount experiments, and T-type domains are well related to mixture experiments. With these stochastic representations,
the corresponding uniform distribution and number-theoretic nets can be generated. This approach seems to be new and is called
order statistics method. Some examples on reliability growth analysis and experimental design are presented.
This work was partially supported by a Hong Kong UGC-RGC grant, the Statistics Research and Consultancy Centre of HK-BU, and
the Chinese Academy of Sciences. |
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Keywords: | discrepancy isotonic restriction Monte Carlo optimization multivariate distribution uniform design |
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