Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions. (English) Zbl 0952.62073
Summary: With order statistics of the uniform distribution on \([0,1]\), 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.
MSC:
| 62K99 | Design of statistical experiments |
| 62F30 | Parametric inference under constraints |
| 62K05 | Optimal statistical designs |
| 65C60 | Computational problems in statistics (MSC2010) |
| 62N05 | Reliability and life testing |
Keywords:
discrepancy; isotonic restriction; Monte Carlo optimization; multivariate distribution; uniform design; reliability growth; order statistics methodReferences:
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