# Question: A nickel titanium alloy is used to make components for jet

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 failure. A test is run at the parts producer to determine the effects of four factors on cracks. The four factors are pouring temperature (A), titanium content (B), heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm ×10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown below.

(a) Estimate the factor effects. Which factor effects appear to be large?

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

(e) Is there an indication that any of the factors affect the variability in cracking?

(d) The residuals show a violation of the assumptions. It appears that the data would be

better fit using two separate models.

(e) It does not appear than any of the variables affect the variability in cracking.

(f) What recommendations would you make regarding process operations? Use interaction and/or main effect plots to assist in drawing conclusions.

(c) yˆ 11.988 1.509A 1.988B 1.798C 0.979D 0.967AB 2.004AC

(a) Estimate the factor effects. Which factor effects appear to be large?

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

(e) Is there an indication that any of the factors affect the variability in cracking?

(d) The residuals show a violation of the assumptions. It appears that the data would be

better fit using two separate models.

(e) It does not appear than any of the variables affect the variability in cracking.

(f) What recommendations would you make regarding process operations? Use interaction and/or main effect plots to assist in drawing conclusions.

(c) yˆ 11.988 1.509A 1.988B 1.798C 0.979D 0.967AB 2.004AC

**View Solution:**## Answer to relevant Questions

The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment. (a) Fill in the blanks in the ANOVA table. You can use bounds on the P-values. (b) How many levels were ...Suppose that the specifications require that the surface area must be between 0.3 and 0.6 cm2/g and that the density must be less than 14 g/cm3. Find a set of operating conditions that will result in a product that meets ...Reconsider the crystal growth experiment from Exercise 14.12. Suppose that x3 = z is now a noise variable, and that the modified experimental design shown in Table 14E.7 has been conducted. The experimenters want the growth ...Consider the first-order model yt = 75 + 10x1 + 6x2 (a) Sketch the contours of constant predicted response over the range –1 ≤ xi ≤ + 1, i = 1, 2. (b) Find the direction of steepest ascent. Suppose that a single-sampling plan with n = 150 and c = 2 is being used for receiving inspection where the supplier ships the product in lots of size N = 3,000. (a) Draw the OC curve for this plan. (b) Draw the AOQ curve ...Post your question