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A light bulb manufacturer wants to maximize bulb lifetime. Four parameters are to be tested: Parameters a and b are the concentrations of a certain alloys in the filament. Parameters c and d are the temperature and speed, respectively, at which the filaments are extruded in the manufacturing process. A three-level experiment is to be used. Levels 1, 2, and 3 correspond to low, medium, and high values of each respective parameter. Taguchi's 9-run design array (as in the learning module) is to be used. For each experimental run, thirty bulbs are tested, and the mean time to failure (MTTF) for each run is recorded as X₁, X₂, etc. These values, in order, are 1318, 1375, 1414, 1490, 1532, 1296, 1455, 1219, and 1266 hours, to four significant digits. (a) Generate a table with the above values configured as a Taguchi 9-run design array (Excel is recommended). Calculate all 12 level averages, i.e. Xal, Xa2, X3, Xb, Xb2.. Хаз (b) Generate four plots, showing the dependence of X on each parameter. The first plot is of level average as a function of variable a, the second is of level average as a function of variable b, etc. For simplicity, the values of a₁, a2, and a3 can be taken as 1, 2, and 3, respectively. Similarly, the values of b₁,b2, and b3 can be taken as 1, 2, and 3, respectively, etc. for all the parameters. For consistency, everybody please use the same scale on the vertical axis for all four plots: 1200 to 1500 hours. Also, use a scatter plot, with both symbols and a smoothed line for all four plots. (c) Based on these experiments alone, which levels of each parameter do you recommend in order to maximize light bulb lifetime? 5 (d) Finally, if you were the engineer conducting these experiments, what (if anything) would you recommend for follow-up experiments, if the budget allows for follow-up tests in which only three of the parameters are varied? I.e., which three parameters would you vary, and at what values (higher, lower, etc.)?

A light bulb manufacturer wants to maximize bulb lifetime. Four parameters are to be tested: Parameters a and b are the concentrations of a certain alloys in the filament. Parameters c and d are the temperature and speed, respectively, at which the filaments are extruded in the manufacturing process. A three-level experiment is to be used. Levels 1, 2, and 3 correspond to low, medium, and high values of each respective parameter. Taguchi's 9-run design array (as in the learning module) is to be used. For each experimental run, thirty bulbs are tested, and the mean time to failure (MTTF) for each run is recorded as X₁, X₂, etc. These values, in order, are 1318, 1375, 1414, 1490, 1532, 1296, 1455, 1219, and 1266 hours, to four significant digits. (a) Generate a table with the above values configured as a Taguchi 9-run design array (Excel is recommended). Calculate all 12 level averages, i.e. Xal, Xa2, X3, Xb, Xb2.. Хаз (b) Generate four plots, showing the dependence of X on each parameter. The first plot is of level average as a function of variable a, the second is of level average as a function of variable b, etc. For simplicity, the values of a₁, a2, and a3 can be taken as 1, 2, and 3, respectively. Similarly, the values of b₁,b2, and b3 can be taken as 1, 2, and 3, respectively, etc. for all the parameters. For consistency, everybody please use the same scale on the vertical axis for all four plots: 1200 to 1500 hours. Also, use a scatter plot, with both symbols and a smoothed line for all four plots. (c) Based on these experiments alone, which levels of each parameter do you recommend in order to maximize light bulb lifetime? 5 (d) Finally, if you were the engineer conducting these experiments, what (if anything) would you recommend for follow-up experiments, if the budget allows for follow-up tests in which only three of the parameters are varied? I.e., which three parameters would you vary, and at what values (higher, lower, etc.)?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A light bulb manufacturer wants to maximize bulb lifetime. Four parameters are to be tested: Parameters a and b are the concentrations of a certain alloys in the filament. Parameters c and d are the temperature and speed, respectively, at which the filaments are extruded in the manufacturing process. A three-level experiment is be used. Levels 1, 2, and 3 correspond to low, medium, and high values of each respective parameter. Taguchi's 9-run design array (as in the learning module) is to be used. For each experimental run, thirty bulbs are tested, and the mean time to failure (MTTF) for each run is recorded as X₁, X₂, etc. These values, in order, are 1318, 1375, 1414, 1490, 1532, 1296, 1455, 1219, and 1266 hours, to four significant digits. (a) Generate a table with the above values configured as a Taguchi 9-run design array (Excel is recommended). Calculate all 12 level averages, i.e. Xal, Xa2, X3, Xb₁‚ õ2, Xd3 (b) Generate four plots, showing the dependence of X on each parameter. The first plot is of level average as a function of variable a, the second is of level average as a function of variable b, etc. For simplicity, the values of a₁, a2, and a3 can be taken as 1, 2, and 3, respectively. Similarly, the values of b₁,b₂, and b3 can be taken as 1, 2, and 3, respectively, etc. ... 3 for all the parameters. For consistency, everybody please use the same scale on the vertical axis for all four plots: 1200 to 1500 hours. Also, use a scatter plot, with both symbols and a smoothed line for all four plots. (c) Based on these experiments alone, which levels of each parameter do you recommend in order to maximize light bulb lifetime? (d) Finally, if you were the engineer conducting these experiments, what (if anything) would you recommend for follow-up experiments, if the budget allows for follow-up tests in which only three of the parameters are varied? I.e., which three parameters would you vary, and at what values (higher, lower, etc.)?
Transcribed Image Text:A light bulb manufacturer wants to maximize bulb lifetime. Four parameters are to be tested: Parameters a and b are the concentrations of a certain alloys in the filament. Parameters c and d are the temperature and speed, respectively, at which the filaments are extruded in the manufacturing process. A three-level experiment is be used. Levels 1, 2, and 3 correspond to low, medium, and high values of each respective parameter. Taguchi's 9-run design array (as in the learning module) is to be used. For each experimental run, thirty bulbs are tested, and the mean time to failure (MTTF) for each run is recorded as X₁, X₂, etc. These values, in order, are 1318, 1375, 1414, 1490, 1532, 1296, 1455, 1219, and 1266 hours, to four significant digits. (a) Generate a table with the above values configured as a Taguchi 9-run design array (Excel is recommended). Calculate all 12 level averages, i.e. Xal, Xa2, X3, Xb₁‚ õ2, Xd3 (b) Generate four plots, showing the dependence of X on each parameter. The first plot is of level average as a function of variable a, the second is of level average as a function of variable b, etc. For simplicity, the values of a₁, a2, and a3 can be taken as 1, 2, and 3, respectively. Similarly, the values of b₁,b₂, and b3 can be taken as 1, 2, and 3, respectively, etc. ... 3 for all the parameters. For consistency, everybody please use the same scale on the vertical axis for all four plots: 1200 to 1500 hours. Also, use a scatter plot, with both symbols and a smoothed line for all four plots. (c) Based on these experiments alone, which levels of each parameter do you recommend in order to maximize light bulb lifetime? (d) Finally, if you were the engineer conducting these experiments, what (if anything) would you recommend for follow-up experiments, if the budget allows for follow-up tests in which only three of the parameters are varied? I.e., which three parameters would you vary, and at what values (higher, lower, etc.)?
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