Applied Engineering Statistics Exam

Homework4.pdf

IE5002 Homework 4

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 experimental 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.

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

design 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 factors 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 condition was replicated

twice. The data are as follows.

IE5002 Homework 4

(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.

(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?