##### Reference no: EM131251595

Consider the leaf spring experiment in Problem 8.7. Suppose that factor E (quench oil temperature) is very difficult to control during manufacturing. Where would you set factors A, B, C, and D to reduce variability in the free height as much as possible regardless of the quench oil temperature used?

Problem 8.7:

Continuation of Problem 8.6. In Exercise 6.6, we found that all four main effects and the two-factor AB interaction were significant. Show that if the alternate fraction (I = - ABCD) is added to the 241 design in Problem 8.6 that the analysis of the results from the combined design produce results identical to those found in Exercise 6.6.

Problem 8.6:

In Example 6.6, a 24 factorial design was used to improve the response rate to a credit card mail marketing offer. Suppose that the researchers had used the 241 fractional factorial design with I = - ABCD instead. Set up the design and select the responses for the runs from the full factorial data in Example 6.6. Analyze the data and draw conclusions. Compare your findings with those from the full factorial in Example 6.6.

Example 6.6:

An article in the International Journal of Research in Marketing ("Experimental Design on the Front Lines of Marketing: Testing New Ideas to Increase Direct Mail Sales," 2006, Vol. 23, pp. 309-319) describes an experiment to test new ideas to increase direct mail sales by the credit card division of a financial services company. They want to improve the response rate to its credit card offers. They know from experience that the interest rates are an important factor in attracting potential customers, so they have decided to focus on factors involving both interest rates and fees. They want to test changes in both introductory and long-term rates, as well as the effects of adding an account-opening fee and lowering the annual fee. The factors tested in the experiment are as follows:

The marketing team used columns A through D of the 24 factorial test matrix shown in Table 6.22 to create 16 mail packages. The +/- sign combinations in the 11 interaction (product) columns are used solely to facilitate the statistical analysis of the results. Each of the 16 test combinations was mailed to 7500 customers, and 2837 customers responded positively to the offers.

Table 6.23 is the JMP output for the screening analysis. Lenth's method with simulated P-values is used to identify significant factors. All four main effects are significant, and one interaction (AB, or Annual Fee × Account Opening Fee). The prediction profiler indicates the settings of the four factors that will result in the maximum response rate. The lower annual fee, no account opening fee, the lower long-term interest rate and either value of the initial interest rate produce the best response, 3.39 percent. The optimum conditions occur at one of the actual test combinations because all four design factors were treated as qualitative. With continuous factors, the optimal conditions are usually not at one of the experimental runs.