TY - JOUR

T1 - Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions

AU - Tian, Guoliang

AU - Fang, Kaitai

N1 - Funding Information:
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.

PY - 1999/5

Y1 - 1999/5

N2 - 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.

AB - 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.

KW - Discrepancy

KW - Isotonic restriction

KW - Monte Carlo optimization

KW - Multivariate distribution

KW - Uniform design

UR - http://www.scopus.com/inward/record.url?scp=0042233438&partnerID=8YFLogxK

U2 - 10.1007/BF02882241

DO - 10.1007/BF02882241

M3 - Article

AN - SCOPUS:0042233438

SN - 1006-9283

VL - 42

SP - 456

EP - 470

JO - Science in China, Series A: Mathematics, Physics, Astronomy

JF - Science in China, Series A: Mathematics, Physics, Astronomy

IS - 5

ER -