Chapter 11.3, Problem 31E

Nickel titanium (NiTi) shape memory alloy (SMA) has been widely used in medical devices. This is attributable largely to the alloy’s shape memory effect (material returns to its original shape after heat deformation), superelasticity, and biocompatibility. An alloy element is usually coated on the surface of NiTi SMAs to prevent toxic Ni release.

The article “Parametrical Optimization of Laser Surface Alloyed NiTi Shape Memory Alloy with Co and Nb by the Taguchi Method” (J. of Engr. Manuf., 2012: 969–979) described an investigation to see whether the percent by weight of nickel in the alloyed layer is affected by carbon monoxide powder paste thickness (C, at three levels), scanning speed (B, at three levels), and laser power (A, at three levels). One observation was made at each factor-level combination [Note: Thickness column headings were incorrect in the cited article]:

1. a. Assuming the absence of three factor interactions (as did the investigators), SSE = SSABC can be used to obtain an estimate of σ². Construct an ANOVA table based on this data.
2. b. Use the appropriate F ratios to show that none of the two-factor interactions is significant at α = .05.
3. c. Which main effects are significant at α =.05?
4. d. Use Tukey’s procedure with a simultaneous confidence level of 95% to identify significant differences between levels of paste thickness.