16 881 Robust System Design Homework 3 The Context of Robust Design and the Principles of Quality Engineering Due Date Monday June 15 1 05 2 55 the first meeting of 16 881 Objectives Reinforce material from Phadke chapters 1 and 2 Tie that material back to fundamental principles from session 1 Apply concepts on the context of robust design in system development Assignment 1 Consider an experiment in which two six sided fair dice are rolled One die is green the other is red Let s model the outcome on the green die as a discrete random variable G and the outcome on the red die as a discrete random variable R and the sum of the two outcomes as a discrete random variable T G R a Sketch the probability mass functions for G and R b Compute the expected value and variance of G and R c Sketch the joint density function for G and R d What is the covariance of G and R e Sketch the probability mass function of T f Compute the expected value and standard deviation T Note Recall that the variance is a measure of the dispersion of a random variable and is defined asVAR X E X E X 2 Similarly the covariance is a measure of the degree of association between two random variables and is defined as COV X Y E X E X Y E Y 2 Repeat all of the steps in problem 1 for a slightly different experiment Two sixsided fair dice are rolled Again one die is green the other is red But this time after the dice are rolled a smurf magically appears and changes the outcome of the red die to match that of the green die 3 Anstron Corporation uses a spring to calibrate the load cells it manufactures The function of the calibration system is to apply 10 Newtons of tensile force to the load cell while an instrument measures the voltage across a Wheatstone bridge of strain gauges within the load cell This voltage is recorded and included in the documentation provided to the customer The records suggest that if the recorded voltage varies from the proper value by more than 0 1 the load cell will be returned costing Anstron Corporation 20 Both the widths of the load cells and the natural lengths of the springs tend to vary about their nominal values of 2cm and 6cm respectively A sample of data suggests that the width of the load cell W has a standard deviation of 2 m the natural length of the spring Lo has a standard deviation of 10 m and the spring constants have a standard deviation of 1x10 3N cm Your job is to design the calibration fixture so as to minimize the quadratic loss due to variation in the applied force F You may anchor the calibration spring at any point within 20 cm from the point of attachment of the load cell to the fixture point A You may choose from among springs with spring constants of 1N cm 2N cm and 3N cm all have a nominal natural length of 6cm a Which spring will you choose b Where will you place the anchor point c What is the expected value of the quality loss due to variation assuming these three noise variables dominate 20cm W Lo A k Load cell Spring Anchor 4 Integration Referring to the figure below compare two cases Case 1 NT and A G are all new technologies and are not robust when they are integrated Case 2 NT and A G are all robust when they are integrated Compare the two cases 1 Problems encountered 2 Fundamental phenomena that underlie the difference in problems encountered Use a little mathematics to make your points more clear Two computer generated pages should be sufficient B1 A1 G1 C1NEW TECHNOLOGY NT D1 F1 E 1