2.4 The change in temperature between a heating element and the next operation in an industrial process depends on a range of factors, such as the distance between the heating element and the downstream operation. There are also a number of noise factors (Table 2.4). The temperature in this downstream operation is important for the result of the operation.

(a) Analyse the data of Table 2.4. Build a mathematical model.

(b) Are there any ways to make the temperature change robust against the noise factors?

(c) In this study, the production rate (units per time unit) was considered as a noise factor. Are there any other alternatives?

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Table 2.4 The temperature drop data of Exercise 2.4. Control factors Noise factors Response Distance Factor Factor Factor Production AT A B C D rate (E) y 150 30 100 20 200 20 100 20 200 20 100 20 200 20 100 20 200 20 150 30 100 40 200 40 200440044200 2800 2 6.2 800 800 800 800 4800 4800 4800 4800 2800 800 800 100 40 4 800 200 40 800 100 40 0 4800 200 40 0 4800 100 40 4 4800 200 40 4 4800 150 30 2 2800 13313II3231I313312 6.1 5.6 9.2 13.5 6.4 10.2 11.5 12.7 7.0 1.6 4.5 6.2 5.9 3.8 4.3 6.3 8.2 6.4