QUESTION 1 [50] In attaching components to an electronic circuit card assembly by a wave-soldering process, solder-joint defects arise. The soldering process involving baking and preheating the circuit card and then passing it through a solder wave by conveyer. Condra (1993, Chapter 7) presented the results of an experiment to reduce solder defects which studied the following seven factors: (A) prebake condition; (B) flux density; (C) conveyer speed; (D) preheat condition; (E) cooling time; (F) ultrasonic solder agitator; and (G) solder temperature. A 1/8 fraction of a full factorial design (i.e., a 27–3 fractional factorial design) was used to study the seven factors each at two levels with three boards from each run being assessed for defects. The response yi, i = 1, 2, 3 was the number of defects on a board. The design and response data are given in Table 5 of Hamada and Nelder (1997) and the variables or factors description is presented in Table 1 below. The data is also presented in the dataset wavesolder in the faraway R package. 1 You can assume that the replicates are independent. (a) Make plots of the number of defects against each of the predictors. Comment on the rela- tionships you see. Check graphically that there is no trend in the replicates. (5) (b) Compute the mean and variance within each group of three replicates. Plot the variance against the mean. Comment on the relationship and the viability of a Poisson model for the response. Repeat the plot, but use a log scale on both axes. Does this plot reveal anything new? Explain your answer. (5) (c) Fit a Poisson model for the number of defects with all predictors included as main effects. What does the deviance of this model say about its fit? (10) (d) Make a plot of the residuals against the fitted values of the model that you have fitted in part (c) and comment on what is seen. Make also a QQ plot of the residuals. Are there any outliers? (5)
y3 Table 1: Variables or factors and their description in wavesolder dataset. Variable Description yi Number of defects in the first replicate Y2 Number of defects in the second replicate Number of defects in the third replicate prebake prebake condition - a factor with levels 1 and 2 flux flux density - a factor with levels 1 and 2 speed conveyor speed - a factor with levels 1 and 2 preheat preheat condition - a factor with levels 1 and 2 cooling cooling time - a factor with levels 1 and 2 agitator ultrasonic solder agitator - a factor with levels 1 and 2 temp solder temperature - factor with levels 1 and 2 (e) Refit the Poisson model but excluding the case with the largest residual. Compute the de- viance. Does this model now fit the data? Explain your answer. (10) (1) Fit a quasi-poisson model with same model formula used in part (c) and excluding the case with the largest residual. Estimate the value of the dispersion parameter. Check the model summary. Now use an F-test to test the significance of each of the predictors. Compare the two sets of tests-one from the model summary and one from the F-test. Are they simi- lar? Explain your answer. Report on which predictors are significant and which level of the significant factors will lead to higher defects. (10) (g) Check the diagnostics for the model that you have fitted in part (f) as in part (d). (5) Note: The paper by Hamada and Nelder (1997) is available in-Additional Resource" section on the module web site.
> library(faraway) > data("wavesolder") > wavesolder yi y2 y3 prebake flux speed preheat cooling agitator temp 1 13 30 26 1 1 1 1 1 1 4 16 11 1 1 2 2 2 2 20 15 20 1 2 1 1 2 2 4 42 43 46 1 2 2 2 1 1 5 14 15 17 1 1 1 2 1 2 6 10 17 16 1 1 2 1 2 1 7 36 29 53 1 2 1 2. 2 1 8 5 16 1 2 1 2 9 29 0 14 2 1 1 2 2 1 10 10 26 9 2 1 2 1 1 2 11 28 173 19 2 2 1 2 1 2 12 100 129 151 2 2 1 2 1 13 11 15 11 2 1 1 1 2 2 14 17 2 2 1 2 2 1 1 15 53 70 89 2 2 1 1 1 16 23 22 7 2 2 2 2 2 2 NI HNMON 00 OHHHHH M ONTO OO 00 Omm N on mO O OO M O NON NNN HHHHHHHNNNNNNNN NNNNNNNNX UNNNNNNNN NONEN NHNHNHNHNHNHNHN NNNNNNNN O VIAWNEO .O O NON 17
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!