Applied Engineering Statistics Exam Exam Date：April 26，5pm-7pm, (UTC+8), Please notice the time zone The attached is my homework sample. You can have a look at it and estimate the difficulty level of

IE5002 Homework 4 1 1. An experiment was designed to identify a better ultrafiltration membrane for separating proteins and peptide drugs from fermentation broth. Two levels of an additive PVP (% wt) and time duration (hours) were investigated to determine the better membrane. The separation values (measured in %) resulting from these exper imental runs are as follows: (a) Compute the estimates of the effects and their standard errors for this design. (b) Construct two -factor interaction plots and comment on the interaction of the factors. (c) Use the t ratio to determine the significance of each effect with α = 0.05. Comment on your findings. (d) Compute an approximate 95% CI for each effect. Compare your results with those in part (a) and comment. (e) From your results in (a) and (b), build a model that relates the separation to the desi gn factors. (f) From your model, determine the optimal settings to maximize the separation. 2. A metal alloy is used to make components for aircraft engines. Cracking is a potentially serious problem in the final part, as it can lead to a non -recoverable failure. The objective of the experiment was to identify the key factors and possibly their interactions which have effects on cracks. Four f actors were considered: pouring temperature (A), titanium content (B), heat treatment method (C), and the amount of grain refiner used (D). A 24 experiment was conducted, and the response of interest was the length of crack (in mm ×10 -2). Each trial condit ion was replicated twice. The data are as follows . IE5002 Homework 4 2 (a) Compute the estimates of the effects. (b) Construct the main effect and two -factor interaction plots. Comment on the plots and the likely important effects . (c) Find the possible process conditions to minimize the variability of the crack length? (d) Find the process conditions to minimize crack length? (e) Can we find the optimum process conditions to minimize both the crack length and its variability?