ADVANCED DESIGN OF EXPERIMENTS — DU B.Sc (hons) Statistics Previous Year Question Papers

DSE 5b -Advanced Design of Experiments B.Sc. (Hons.) Statistics under NEP-UGCF Derive the analysis of variance for one-way classified data per cell under a random effects model, stating clearly the mathematical model, the hypothesis to be tested, and the underlying assumptions. Also, draw the ANOVA table. An engineer is studying the mileage performance characteristics of five types of gasoline additives. In the road test, he wishes to use cars as blocks. However, because of a time constraint, he must use an incomplete block design. He runs the balance design with the five blocks that follow. Identify the parameters of the design used to obtain the following data. C.arry out the complete intra-block analysis of the data from this experiment (use cr = 0.05) and draw conclusions. 3. (a) (b) Define the term MOLS. Generate the elements ofGF(7) and construct the complete set of MOLS of order 7. Use orthogonal Latin squares of size 4 to construct the BIBD with .. 4. (a) Letv = A = 7, r = k = 3.ConstructaBIBDwiththeseparanetersuslng the method of differences. Derive a residual BIBD for the resultant BIB.D and write its parameters. (b) Construct a BIBD by taking (1, 3, 4, 5, 9) as the initial block under modulo 1 I . What are the parameters of the resultant design? Write its incidence matrix. 5. (a) Define a response surface design. Obtain the estimates of the unknown parameters of a first-order model, using the principle of least sq-uares. ' Obtain their variances and covariances. (b) Construct a rotatable CCD in two variables with N = 12 runs, such that the design can be blocked orthogonally. into two blocks. 6. (a) What is meant by Mixture experiments? Define the q - 1-dimensional factor space for q = 3. List the 20 blends that comprise a{4,3}simplex-lattice and plot them on the appropriate factor space. Suggest the appropriate model for the design. (b) Define a simplex-c:ntroid design. How is it different from a simplex-latticedesign?Forathree-componentsimplex-centroiddesign,expressthe 2q -1 parameters in the associated polynomial as linear functions of 1:he expected responses 77i, apij and 77ijk.