References
- Kamoun , A. , Chaabouni , M. , Sergent , M. and Phan-Tan-Luu , R. 2002 . Mixture design applied to the formulation of hydrotropes for liquid detergents . Chemometr. Intell. Lab. Syst , 63 ( 1 ) : 69 – 79 . (doi:10.1016/S0169-7439(02)00037-0)
- Kanjilal , P. , Majumdar , S. K. and Pal , T. K. 2004 . Prediction of submerged arc weld–metal composition from flux ingredients with the help of statistical design of mixture experiment . Scand. J. Metall , 33 : 146 – 159 . (doi:10.1111/j.1600-0692.2004.00679.x)
- Piepel , G. F. and Cornell , J. A. 2008 . A catalog of mixture experiment examples BN-SA-3298, Rev. 16.0, Battelle, Pacific Northwest Division, Richland, Washington
- Scheffé , H. 1958 . Experiments with mixtures . J. Roy. Statist. Soc. Series B , 20 ( 2 ) : 344 – 360 .
- Scheffé , H. 1963 . Simplex centroid designs for experiments with mixtures . J. Roy. Statist. Soc. Series B , 25 ( 2 ) : 235 – 263 .
- Nigam , A. K. 1970 . Block designs for mixture experiments . Ann. Math. Statist , 41 : 1861 – 1869 . (doi:10.1214/aoms/1177696687)
- Nigam , A. K. 1976 . Corrections to blocking conditions for mixture experiments . Ann. Statist , 47 : 1294 – 1295 . (doi:10.1214/aos/1176343663)
- John , P. W.M. 1984 . Experiments with mixture involving process variables . Tech. Rep. 8, Center for Statistical Sciences, University of Texas, TX , : 1 – 17 .
- Czitrom , V. 1988 . Mixture experiments with process variables: D-optimal orthogonal experimental designs . Comm. Statist. Theory Methods , 17 : 105 – 121 . (doi:10.1080/03610928808829613)
- Czitrom , V. 1989 . Experimental design for four components with process variables . Comm. Statist. Theory Methods , 18 : 4561 – 4581 . (doi:10.1080/03610928908830175)
- Czitrom , V. 1992 . Note on mixture experiments with process variables . Comm. Statist. Simulation Comput , 21 : 493 – 498 . (doi:10.1080/03610919208813031)
- Draper , N. R. , Prescott , P. , Lewis , S. M. , Dean , A. M. , John , P. W.M. and Tuck , M. G. 1993 . Mixture designs for four components in orthogonal blocks . Technometrics , 35 : 268 – 276 . (doi:10.1080/00401706.1993.10485322)
- Chan , L. Y. and Sandhu , M. K. 1999 . Optimal orthogonal block designs for a quadratic mixture model for three components . J. Appl. Statist , 26 ( 1 ) : 19 – 34 . (doi:10.1080/02664769922629)
- Ghosh , S. and Liu , T. 1999 . Optimal mixture designs for four components in orthogonal blocks . J. Statist. Plann. Infer , 78 : 219 – 228 . (doi:10.1016/S0378-3758(98)00215-8)
- Prescott , P. , Draper , N. R. , Dean , A. M. and Lewis , S. M. 1993 . Mixture designs for five components in orthogonal blocks . J. Appl. Statist , 20 ( 1 ) : 268 – 276 . (doi:10.1080/02664769300000008)
- Lewis , S. M. , Dean , A. M. , Draper , N. R. and Prescott , P. 1994 . Mixture designs for q components in orthogonal blocks . J. Roy. Statist. Soc. Series B , 56 : 457 – 467 .
- Aggarwal , M. L. , Sarin , V. and Singh , P. 2002 . Optimal orthogonal block designs in two blocks for Becker's mixture models in three and four components . Statist. Prob. Lett , 59 : 385 – 396 . (doi:10.1016/S0167-7152(02)00237-7)
- Aggarwal , M. L. , Singh , P. and Gupta , N. 2004 . Orthogonal block designs in two blocks for second degree K-model . Statist. Prob. Lett , 66 : 423 – 434 . (doi:10.1016/j.spl.2003.11.009)
- Becker , N. G. 1968 . Models for the response of a mixture . J. Roy. Statist. Soc. Series B , 30 : 349 – 358 .
- Becker , N. G. 1978 . Models and designs for experiments with mixtures . Austral. J. Statist , 20 : 195 – 208 . (doi:10.1111/j.1467-842X.1978.tb01102.x)
- Chen , J. J. , Li , L.-A. and Jackson , C. D. 1996 . Analysis of quantal response data from mixture experiments . Environmentrics , 7 : 503 – 512 . (doi:10.1002/(SICI)1099-095X(199609)7:5<503::AID-ENV227>3.0.CO;2-E)
- Draper , N. R. and Pukelshiem , F. 1998 . Mixture models based on homogenous polynomials . J. Statist. Plann. Infer , 71 : 303 – 311 . (doi:10.1016/S0378-3758(98)00012-3)
- Draper , N. R. and Pukelshiem , F. 1999 . Kiefer ordering of simplex designs for first- and second-degree mixture models . J. Statist. Plann. Infer , 79 : 325 – 348 . (doi:10.1016/S0378-3758(98)00263-8)
- Draper , N. R. , Heilgers , B. and Pukelshiem , F. 2000 . Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients . Ann. Statist , 28 ( 2 ) : 578 – 590 . (doi:10.1214/aos/1016218231)
- Singh , P. 2003 . Optimal orthogonal designs in two blocks for Darroch and Waller's quadratic mixture model in three and four components . METRON – Int. J. Statist , LXI ( 3 ) : 419 – 430 .
- Aggarwal , M. L. , Singh , P. , Sarin , V. and Husain , B. 2009 . Mixture designs in orthogonal blocks using F-squares . METRON – Int. J. Statist , LXVII ( 2 ) : 105 – 128 .
- Lee , H. H. and Warner , J. C. 1935 . The system biphenyl–bibenzyl–naphthalene. Nearly ideal binary and ternary systems . J. Am. Chem. Soc , 57 : 318 – 321 . (doi:10.1021/ja01305a025)
- Snee , R. D. 1973 . Techniques for the analysis of mixture data . Technometrics , 15 : 517 – 528 . (doi:10.1080/00401706.1973.10489078)
- Hilgers , R.-D. 2000 . D-optimal design for Becker's minimum polynomial . Statist. Probab. Lett , 49 : 175 – 179 . (doi:10.1016/S0167-7152(00)00046-8)
- Cornell , J. A. 2002 . Experiments with mixtures , 3 , New York : John Wiley .
- Prescott , P. , Dean , A. M. , Draper , N. R. and Lewis , S. M. 2002 . Mixture experiments: Ill-conditioning and quadratic model specification . Technometrics , 44 : 260 – 268 . (doi:10.1198/004017002188618446)
- Finney , D. J. 1945 . Some orthogonal properties of 4×4 and 6×6 latin squares . Ann. Eugen , 12 : 213 – 219 .
- Finney , D. J. 1946a . Orthogonal partitions of 5×5 latin squares . Ann. Eugen , 13 : 1 – 3 . (doi:10.1111/j.1469-1809.1946.tb02335.x)
- Finney , D. J. 1946b . Orthogonal partitions of 6×6 latin squares . Ann. Eugen , 13 : 184 – 196 . (doi:10.1111/j.1469-1809.1946.tb02357.x)
- Freeman , G. H. 1966 . Some non-orthogonal partitions of 4×4, 5×5, and 6×6 latin squares . Ann. Math. Statist , 37 : 661 – 681 . (doi:10.1214/aoms/1177699460)
- Addleman , S. 1967 . Equal and proportional frequency squares . J. Amer. Statist. Assoc , 62 : 226 – 240 . (doi:10.1080/01621459.1967.10482903)
- Hedayat , A. and Sieden , E. 1970 . F-squares and orthogonal F-squares design: A generalization of latin square and orthogonal latin squares design . Ann. Math. Statist , 41 : 2035 – 2044 . (doi:10.1214/aoms/1177696703)
- Hedayat , A. , Raghavarao , D. and Sieden , E. 1975 . Further contributions to the theory of F-squares design . Ann. Statist , 3 : 712 – 716 . (doi:10.1214/aos/1176343068)
- Laywine , C. F. 1989 . A geometric construction for sets of MOFS . Utilas Mathematica , 35 : 95 – 102 .