Two controllable factors, temperature and pressure, are each kept at three levels to determine their impact on the ducti
Posted: Mon Nov 15, 2021 10:59 am
Two controllable factors, temperature and pressure, are each
kept at three levels to determine their impact on the ductility of
an alloy being produced. The temperature levels are 150, 250, and
300 0C, respectively. Pressure is controlled at 50,100 and 150
kg/cm2. Each of the nine treatments is replicated five (5) times.
The ductility of the produced alloy is shown in table 1. The higher
the value, the more ductile the alloy.
1) Summarize the information of two controllable factors in tabular
form and calculate a correction factor for the two factorial
randomized block design. [11 marks]
2) Calculate the error sum of squares for the observations and
effects due to blocks is negligible. (Show all working)
[14 marks] 3) Validate all calculated sum of squares
in question 2 using Minitab software, and write the results in
ANOVA tabular. [5 marks]
4) Test whether the interaction effects between temperature and
pressure are significant at the 5% level of significance.
[8 marks]
5) What are the desirable setting of the process temperature and
pressure if a ductile alloy is preferred? , use interaction plot to
respond to this question [3 marks]
6) Find a 90% confidence interval for the mean ductility when
the process temperature is set at 150 0C and pressure of 150
kg/cm2. [4 marks]
7) Find a 95% confidence interval for the difference in mean
ductility for a process temperature of 2500C and pressure of
150kg/cm2 versus a process temperature of 300 0C and pressure 100
kg/cm2 and make inferences about the results. [4
marks]
kept at three levels to determine their impact on the ductility of
an alloy being produced. The temperature levels are 150, 250, and
300 0C, respectively. Pressure is controlled at 50,100 and 150
kg/cm2. Each of the nine treatments is replicated five (5) times.
The ductility of the produced alloy is shown in table 1. The higher
the value, the more ductile the alloy.
1) Summarize the information of two controllable factors in tabular
form and calculate a correction factor for the two factorial
randomized block design. [11 marks]
2) Calculate the error sum of squares for the observations and
effects due to blocks is negligible. (Show all working)
[14 marks] 3) Validate all calculated sum of squares
in question 2 using Minitab software, and write the results in
ANOVA tabular. [5 marks]
4) Test whether the interaction effects between temperature and
pressure are significant at the 5% level of significance.
[8 marks]
5) What are the desirable setting of the process temperature and
pressure if a ductile alloy is preferred? , use interaction plot to
respond to this question [3 marks]
6) Find a 90% confidence interval for the mean ductility when
the process temperature is set at 150 0C and pressure of 150
kg/cm2. [4 marks]
7) Find a 95% confidence interval for the difference in mean
ductility for a process temperature of 2500C and pressure of
150kg/cm2 versus a process temperature of 300 0C and pressure 100
kg/cm2 and make inferences about the results. [4
marks]