QUESTION 5 [14]
Suppose that temperature and reaction time are identified as important factors in the yield of a chemical process. Currently, the process operates at a temperature of 100โ and a 65-minute reaction time. In an effort to reduce costs and improve yield, the plant manager wants to determine if changing the temperature to 115โ and reaction time to 80 minutes will have any significant effect on the percent yield and, if so, to identify the best levels of these factors to optimize the yield.
For this experiment, there are four different treatment combinations as shown below:
Treatment Temperature Time
A 100โ (low) 65 minutes (low)
B 115โ (high) 65 minutes (low)
C 100โ (low) 80 minutes (high)
D 115โ (high) 80 minutes (high)
The following yield results, as shown below, were obtained (with 2 observations for each treatment):
Treatment Temperature Time Yield (%)
A (low, low) 100โ 65 minutes 85
B (high, low) 115โ 65 minutes 91
C (low, high) 100โ 80 minutes 89
D (high, high) 115โ 80 minutes 82
(a) Determine the main effect of temperature. (4)
(b) Determine the main effect of reaction time. (4)
(c) What's your conclusion on the main effect calculations in (a) and (b)? (2)
(d) Determine the temperature and reaction time interaction effect. (4)
Additional formulae:
(1) u-chart formulae:
(a) UCL = ยต + 3โ(ยต/n)
(b) LCL = ยต - 3โ(ยต/n)
(2) Factorial Experiments
(a) Main effect = (Average response at high level) - (Average response at low level).
(b) Interaction effect = (Average response with both factors at the same level) - (Average response with both factors at opposite levels).
(3) The Taguchi Loss formulae:
(a) Loss function: L(x) = k(x - T)^2
(b) EL(x) = k(ฯ^2 + D^2).