STAT 496, Spring 2005Homework Assignment #71. An experiment involving a wire bonder is reported in “How to Optimize and Control the Wire BindingProcess: Part I” by Scheaffer and Levine, Solid State Technology, November, 1990. The five factorsand levels are given below.LevelsFactor Low (—) High ( + )A: Constant Velocity 0.6 in./sec 1.2 in./secB: Temperature 150oC 200oCC: Bond Force 80 g 120 gD: Ultrasonic Power 120 mW 200 mWE: Bond Time 10 ms 20 msThe response variable, Y, was a force (in grams) required to pull wire bonds made on the machineunder a particular combination of levels of the factors. The levels and responses for the 25−1fractionalfactorial experiment are given below.Treatment FactorCombination A B C D E=ABCD Force, ge − − − − + 8.5a + − − − − 7.9b − + − − − 7.7abe + + − − + 8.7c − − + − − 9.0ace + − + − + 9.2bce − + + − + 8.6abc + + + − − 9.5d − − − + − 5.8ade + − − + + 8.0bde − + − + + 7.8abd + + − + − 8.7cde − − + + + 6.9acd + − + + − 8.5bcd − + + + − 8.6abcde + + + + + 8.6(a) Give the defining relation.(b) What resolution is this design?(c) Estimate the effect of each of the factors and interactions. For each estimated effect give the effectname and all aliases.(d) Using a normal probability plot identify, with name and aliases, effects that appear to be signifi-cant.(e) Suppose that in addition to the 16 points in the fractional factorial, 5 runs were made at constantvelocity of 0.9 in./sec, a temperature of 175oC, a bond force of 100 g, a power of 160 mW and abond time of 15 ms. The observed pull strengths at these points were: 8.1, 8.6, 8.0, 8.7, & 8.1.Use these to come up with a critical effect size. Which effects in (c) are significant?(f) Each effect name has an alias. To what factor or combination of factors do you attribute eachsignificant effect?1(g) Give a prediction equation using those effects deemed significant in (e) and identified in (f). Besure to define, explicitly, each variable in your equation.(h) What would your recommendation be for the operating conditions of this machinery to obtainthe highest pull force? Give a prediction and prediction interval for these operating conditions.2. An engineer,who is planning a 27−3fractional factorial has in mind two separate choices of generators.Choice 1: E=ABCD, F=ACD, G=BCDChoice 2: E=ABC, F=BCD, G=ACD(a) Write out the entire defining relation for both each choice.(b) Which choice is most appealing and why?(c) Give the treatment combinations, in terms of −1’s and +1’s and the shorthand notation, e.g. (1),bc, etc. for your most appealing choice. Use the attached sheet.3. An experiment is conducted on the efficiency of a refrigeration system using R12, essentially Freon.In the experimental test stand, water temperature simulates the ambient temperature outside a housewhile air temperature simulates the ambient temperature inside a house. Three levels of each temper-ature are used in a full factorial. The data appear below.Air Temperature (oF )WaterTemperature (oF ) 55 60 652.99 3.07 3.1670 2.96 3.03 3.132.96 3.02 3.132.76 2.82 2.9080 2.74 2.81 2.912.72 2.80 2.922.55 2.59 2.6790 2.54 2.58 2.642.53 2.57 2.64(a) Construct main effect and interaction plots and comment on the possible impact of each factorand the interaction. Comment on whether there appears to be a linear or curved response betweeneach of the factors and the response.(b) Fit a response surface model using orthogonal polynomials (JMP does not automatically useorthogonal polynomials to do the fit of a response surface. Therefore the output from JMP willnot give you the analysis asked for in this question. If you enter the orthogonal polynomialcoefficients as separate columns in JMP, use Fit Model and Add each column into the ConstructModel Effects, the JMP output will match what is being asked for in this question). Give theprediction equation. Be sure to explicitly define all variables in the equation.(c) Predict the efficiency for the test stand operating with a water temperature of 85 and an airtemperature of 65.(d) Reduce the model to include only those terms that are statistically significant. Again give theprediction equation and predict the efficiency for the test stand operating with a water temperatureof 85 and an air temperature of 65.(e) Contour and response surface (wireframe) plots of the full quadratic model and the reduced modelare given on the next pages. What do these plots indicate about the effects of water temperatureand air temperature on the refrigeration test stand efficiency?234Treatment Factorrun Combination A B C D E F