# Analysis of Variance

**Topics:**Analysis of variance, Design of experiments, Normal distribution

**Pages:**2 (594 words)

**Published:**June 14, 2013

Problems 6.15, 6.22

Q6.15. a nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to non-recoverable failures. A test is run at the parts producer to determine the effect of four factors on the cracks. The four factors are: Pouring temp (A), Titanium content (B), Heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 2^4 design are run and the length of cracks (in mm x10^-2) induced in a sample coupon subjected to a standard test. a) Estimate the factor effects, which factor effects appear to be large.

(Half normal plot showing the significant factors)

From the minitab output given above after conducting an analysis of factorial design and showing the half normal plot it appear that the Pouring temp (A), Titanium content (B), Heat treatment method (C), and amount of grain refiner used (D) are all large and significant as well as the interaction between Pouring temp (A) and Titanium content (B), and interaction between Titanium content (B) and Heat treatment method (C), and finally the interaction between Pouring temp (A), Titanium content (B) and Heat treatment method (C). A, B, C, D, A&B, B&C, and A&B&C

b) Conduct an analysis of variance. Do any of the factors affect the cracking? Use α = 0.05.

From the analysis of variance minitab output given above we can conclude that the following factors affect the cracking for having a p-value < α=0.05: * Factor (A) Pouring temperature

* Factor (B) Titanium content

* Factor (C) Heat treatment method

* Factor (D) Grain refiner

* Interaction of (A) and (B)

* Interaction of (B) and (C)

* Interaction of (A), (B) and (C)

c) Write down the regression model that can be used to predict crack length as a function of the significant main effect and interaction you have identified in part (b).

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