Construction of optimal designs to increase the power of the multiresponse lack of fit test (Q1094053)

The authors have introduced two design criteria to increase the power of the multivariate lack of fit test, namely, \(\Lambda_ 1\) and \(\Lambda_ 2\)-optimality criteria. It is an extension of the second author's work, Technometrics 27, 213-218 (1985) on single response function to the multiresponse model. They have also considered likelihood ratio, Pillai's trace and Hotelling-Lawley's trace test statistics. \(\Lambda\) \({}_ 1\)-optimal designs can only be obtained under certain conditions. Hence, \(\Lambda_ 2\)-optimality has been dealt with in details. Application of the theory is demonstrated through real industrial problems.