16 881 Robust System Design Final Exam This exam is composed of 4 essays followed by 20 short answer questions 24 questions total The essays are each worth 10 and the short answers are each worth 3 Therefore the essays comprise 40 of the credit and the short answers comprise the other 60 You have 2 hours Divide your time accordingly perhaps 10 minutes per essay and three minutes per short answer leaving 20 minutes of buffer for review at the end When asked for an estimate any answer correct to within 10 earns you full credit 1 10 In robust design what is a dynamic system What is ideal function in a dynamic system Give an example of ideal function in a dynamic system from an engineering context 1 of 10 2 10 What are noise factors What is a compound noise factor Under what conditions would you recommend using a compound noise factor 2 of 10 3 10 Describe an engineering example of a system integration problem caused by insufficient robustness of the system s components or subsystems Explain what failure modes occurred what noise factors were involved and how system level interactions came into play 3 of 10 4 10 Your engineering team is involved in a product development project imagine a project that is similar to those in your company You decide to apply robust parameter design techniques to a critical subsystem Based on the factor effect plots you choose a set of control factor levels that are predicted to improve the S N ratio by 12dB Upon running the confirmation experiment you find that the rise in signal to noise ratio is only 6dB What might have caused this difference between prediction and confirmation As the leader of the product development team what would you do in this situation Why 4 of 10 Questions 5 10 below refer to the following scenario You are an engineer at ALDOA incorporated and you are concerned with the effects of precipitation heat treatment on the yield strength Y of a new aluminum alloy Customer surveys indicate that perceived quality loss is inversely proportional to the square of Y You wish to determine the effects on Y of the following control factors Oven temperature high medium low Oven size small medium large Position of the specimen in the oven on the floor on a low rack on a high rack Aging time short medium long Quenching liquid water oil Quenching liquid temperature high medium low 5 3 Which signal to noise ratio would you use to guide the design 6 3 How many experiments are required if you want to determine the main effects only and you use a one factor at a time experimental design with three replicates of each experimental treatment 7 3 If you want to determine the main effects only and you wish to use one of the standard orthogonal arrays listed in Appendix C of Phadke which one would you choose 8 3 How much more reliable is your estimate of the effect of oven temperature on S N ratio when using the orthogonal array selected problem 7 as compared to the one factor at a time experiment problem 6 Again assume three replicates are performed for each experimental treatment 9 3 In order to conduct a full factorial experiment how many experiments would you would need to conduct Again assume three replicates are performed for each experimental treatment 10 3 If it is likely that there is a significant interaction between quenching liquid and quenching liquid temperature How will you ensure that your experimental plan will allow you to estimate this interaction 5 of 10 The factor effect plots below represent the results of an orthogonal array based experiment These plots are the basis of the questions 11 14 below 11 3 Which control factor should be used as the scaling factor assuming the additive model holds 12 3 What settings of the other control factors will maximize the S N ratio assuming the additive model holds 13 3 What will be the predicted S N ratio at the optimal settings selected in problem 12 above Estimate your answer from the graphs 14 3 After optimizing the S N ratio what level should be selected for the scaling factor in order to place the mean response of the system at 31 Ohms Assume an additive model holds for the mean response of the system S N Ratio dB Factor Effects on the S N Ratio 18 17 16 15 14 13 12 11 10 A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 Resistance Ohms Factor Effects on the Mean 34 33 32 31 30 29 A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 6 of 10 The data below represent the results from an L4 23 The third column was left unassigned This data is the basis of questions 15 17 below Exp no 1 2 3 4 Control Factors A B e 1 1 1 1 2 2 2 1 2 2 2 1 7 dB 17 dB 5 dB 19 dB 15 3 Sketch the AXB interaction plot 16 3 If you pool the variance due to the unassigned column the third column what will be the F ratio of control factor B 17 3 Do you judge the interaction between factors A and B to be significant 7 of 10 Questions 18 and 19 refer to the scenario described below The circuit below is an amplifier circuit including an op amp with a finite input resistance Ri The gain v2 vs of the circuit is known to be v2 k R 2 R i v S R 2 R i R 1 R i R 1 R 2 k R 1 R i The noise factors are R1 1k 1 R2 1k 1 Ri 50k 1 k 100 10 18 3 Estimate the standard deviation of the gain v2 vs Remember any answer within 10 gets you full credit 19 3 The average quality loss per circuit is 0 05 and is due entirely to variance in the gain v2 vs assume the average gain is very close to the target value Loosening the tolerance to 5 on any resistance will save 0 01 per circuit Which tolerances would you relax 8 of 10 Questions 20 24 refer to the following scenario You are designing a high bypass turbofan engine for a small commercial transport Pilots seem to fly more safely and efficiently when the thrust delivered by the engine is consistent for any given throttle position under a wide range of angles of attack Your design team performs a continuous continuous dynamic signal to noise analysis with throttle position as the signal factor and thrust as the response Angle of attack is the only noise factor induced in the experiment The following data were collected Throttle position 1 full throttle 5 degrees 7 9 x103lbs 11 0x103lbs 16 0x103lbs 10 degrees 7 0x103lbs 10 5x103lbs 14 1x103lbs 20 degrees 6 1x103lbs 9 9x103lbs 12 1x103lbs 20 3 Estimate the slope of the least squares regression line Remember to include units 21 …