Objectives ? Review the format and expectations for the final exam ? Review material needed to succeed on the final exam ? Set the material from the course in the context of the product realization process ? Answer questions 16.881 MIT Importance of the Final ? The course grade is determined by – 40% term project Balance? – 30% final exam – 20% homework – 10% quizzes Dominates ? The final shows how you’ve learned over time – Did the home works and quizzes stick? 16.881 MIT Format of the Final Exam ? 4 essay questions (10% each) ? 20 short answer questions (3% each) ? Which means its – 40% Essay – 60% Short answer ? 2 Hours -- I’d suggest – 10 minutes per essay – 3 minutes per short answer – 20 minute buffer / review MIT16.881 Final Exam Rules ? Open book ? Open notes ? Solutions to homework, quizzes -- OK ? Calculators -- probably helpful ? Laptop computers -- fine, but not needed 16.881 MIT Essay Questions ? Emphasize the big picture and concepts ? Composed of several inter-related questions ?Example – What is a scaling factor? – What are the properties of a good scaling factor? – Provide an example of a scaling factor – If you found that there was no control factor with the desired properties, what would you do? – Tell me anything you know about scaling factors that you consider essential to practicing robust design. 16.881 MIT Expectations on Essay Questions ? Answer the questions! ? Make your responses concise – About 3 sentences per question if possible ? Make the answer complete but avoid a shot gun approach – Points will be deducted for imprecise statements ? Examples should have engineering relevance ? Examples should preferably be from some area you know from experience rather than from a text 16.881 MIT Short Answers ? Fairly similar to quizzes in format, difficulty, and sometimes in content ? No multiple choice or true / false ? Usually come in clusters of 3-5 ? Relate to a scenario, data table, graphs … ? Usually have a “right answer” ? Often require estimation 16.881 MIT Expectations on Short Answers ? Right answer ± 10% gets you full credit – So simplify and estimate when appropriate ? Right procedure gets you 2/3 credit – So show your work if you have time ? A reasonable attempt gets you 1/3 credit – So explain your assumptions 16.881 MIT Short Answer -- Example ? The data below represent the results from an L 8 (2 7 ). Control Factors Exp no. A B C D e e F η 1 1 1 1 14 2 1 1 2 18 3 1 2 2 19 4 1 2 1 10 5 2 1 2 18 6 2 1 1 12 7 2 2 1 13 8 2 2 2 19 The fifth and sixth columns were left 1 1 1 1 2 2 2 1 2 1 1 2 1 2 2 2 1 2 1 2 2 1 2 2 2 2 1 1 1 1 2 1 unassigned. ? What is the factor effect f 1 ? ? Estimate the sum of squares due to the mean. ? You wish to study interaction between control factors A and D and also between factors F and B. Will this design allow you to determine the effect 16.881 of these two interactions? MIT What is Fair Game ? Any concept or technique described in Phadke ? Any material in the lecture notes ? Any material in quizzes & home works ? Questions requiring original thought on subtle topics not explicitly discussed in class 16.881 MIT High Probability Topics ? Ideal function ? Noise factors, control factors, signal factors, responses ? Design for additivity ? Interaction plots ? Selection of appropriate OAs ? Dummy levels 16.881 MIT High Probability Topics ? Orthogonality ? The balancing property ? Estimating variance of responses ? Quality loss functions ? ANOVA (Taguchi style) ?ANOM ? Design of dynamic systems 16.881 MIT High Probability Topics ? Compounding factors ?Noise strategies ? System integration & RD ? Counting DOF of a system ? Selecting an OA to suit a scenario ? Studying interactions in OAs ? Tolerance design (insofar Phadke covers it) 16.881 MIT High Probability Topics ? Failure modes & RD ? Confirmation experiments ? Column merging ? Factor effect plots ? The additive model ? Prediction based on the additive model ? Sliding levels 16.881 MIT High Probability Topics ? Pooling and F ratios ? Choosing a proper S/N ratio ? Interpreting S/N ratios ? Making engineering and economic judgements based on data ? Selecting quality characteristics ? Selecting control factors 16.881 MIT Proactive Problem Solving Example Essay ? You are the manager of a new product development program. 75% of the technology in the product is established and 25% is being fielded for the first time. ? What techniques from this class would you apply? ? At what stages would you apply them? ? How would your efforts differ between the new technology and the established technology? 16.881 MIT Robust Design and Failure Modes Example Essay ? When variance in a quality characteristic is too large, describe how adjustment of the mean can lead to chasing the problem from one failure mode to another (and often back again). ? Give an example of this phenomenon from an engineering context. ? If your product has multiple quality characteristics, how does this impact this phenomenon? ? How can the architecture of the system aggravate or ameliorate this problem? 16.881 MIT MIT16.881 Noise Factors Example Short Answer Group ? Air Shock Absorber -- h and D vary by 1% ? Estimate the ratio of the contribution of h and D 2 to variance in t ? Estimate the ratio of σ t to t F D hD t π ρπ 2 2 2 3 1 = D 2 D 1 F h ρ System Integration Sample Essay ? Describe how lack of robustness in subsystems can lead to difficulties in system integration. ? Give an example of a system integration problem due to lack of robustness. ? If a robust design effort reduces the variance in all the subsystems, how will this effect the variance of the system? ? How is this effect a function of system scale and system architecture? 16.881 MIT Noise Strategy Sample Essay ? What is a compound noise factor? ? When would you use a compound noise factor? ? What is an outer orthogonal array? ? Compare the strategies of compounding noise factors with employing an outer array of noise with regard to: ? Its effect on selection of control factor levels ? Tolerance design decisions ? Decision to field or not to field the system ? Discuss any alternate noise strategies you might consider 16.881 MIT Parameter Design Example Problem ?Given – Description of engineering scenario – Control factors and levels ? Questions ? Which signal-to-noise ratio would you use? ? How many experiments are required? ? What is the smallest experiment that will allow you to resolve the main effects? ? What is the gain in experimental efficiency by switching from one-factor-at-a-time to orthogonal array based experiments? ? It is likely that there is a significant interaction between A and B. How will you ensure that your experimental plan can resolve this interaction effect? 16.881 MIT Next Steps ? Final exam – 8AM (Sharp!) -10AM ? First off-campus session – 3:03-4:55 ? Each student may resubmit up to three quizzes and/or home works by Monday 13 July (grades will be averaged with the original grades) 16.881 MIT