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 100 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 115 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 optimise the yield. For this experiment there are four different treatment combinations as shown below. Treatment Temperature Time A 100 (low) 65 minutes (low) B 115 (high) 65 minutes (low) C 100 (low) 80 minutes (high) D 115 (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) 100 65 minutes 85 B (high, low) 115 65 minutes 91 C (low, high) 100 80 minutes 89 D (high, high) 115 80 minutes 82

(a) Determine the main effect of temperature. (4) (b) Determine the main effect of reaction time. (4) (c) Whats your conclusion on the main effect calculations in (a) and (b)? (2)

(d) Determine the temperature and reaction time interaction effect. (4) EBQCI4A Additional formulae (1) u-chart formulae: EBQCI4A Semester Test 1 Questions 2023-1 Page 4 of 14 (a) = = (b) UCL n = + 3 a n (c) LCL n = - 3 a 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 ( 2 + D 2 ).