Evaluating lead-free solders . Traditionally, solders used in electronics assemb

Question

Evaluating lead-free solders. Traditionally, solders used in electronics assembly are made with lead. Due to numerous environmental hazards associated with lead solders (e.g., groundwater contamination and breathing in of fine lead-bearing particles), engineers are developing lead-free solders. In Soldering & Surface Mount Technology (Vol. 13, 2001), researchers compared the traditional tin–lead alloy solder to three lead-free alloys: tin–silver, tin–copper, and tin–silver–copper. A measure of plastic hardening (Nm/m2) was obtained for each solder type at each of six different temperatures. The data are given in the table.

LEADSOLDER Tin-Silver- Temperature Tin-Lead Tin-Silver Tin-Copper Copper 23°C 50.1 33.0 14.9 41.0 50°C 24.6 27.7 10.5 20.7 75°C 23.1 10.7 9.3 17.1 100°C 1.8 9.0 8.8 8.7 125°C 1.1 4.9 5.4 7.1 150°C 0.3 3.2 5.0 4.9 Source: Harrison, M. R., Vincent, J. H., and Steen, H. A. H. "Lead-free reflow soldering for electronics assembly." Soldering & Surface Mount Technology, Vol. 13, No. 3, 2001 (Table X)

Explanation / Answer

> data=c(50.1,33,14.9,41,24.6,27.7,10.5,20.7,23.1,10.7,9.3,17.1,1.8,9,8.8,8.7,1.1,4.9,5.4,7.1,0.3,3.2,5.0,4.9)
> group1=c(rep(1,4),rep(2,4),rep(3,4),rep(4,4),rep(5,4),rep(6,4))
> group2=rep(1:4,6)
> df=data.frame(data,group1,group2)
> df$group1=as.factor(group1)
> df$group2=as.factor(group2)
> model=aov(data~group1+group2,data=df)
> summary(model)
Df Sum Sq Mean Sq F value Pr(>F)   
group1 5 2910.8 582.2 11.038 0.000134 ***
group2 3 240.6 80.2 1.521 0.249899   
Residuals 15 791.1 52.7
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Since p-value for group2 > 0.05, we can conclude that the means of the values of different soldering are not significantly different but since p-value for group1<0.05, we can say that the means of the values for different temperatures are signficantly different.

> TukeyHSD(model)
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = data ~ group1 + group2, data = df)

$group1
diff lwr upr p adj
2-1 -13.875 -30.55913 2.8091316 0.1325039
3-1 -19.700 -36.38413 -3.0158684 0.0165127
4-1 -27.675 -44.35913 -10.9908684 0.0008722
5-1 -30.125 -46.80913 -13.4408684 0.0003673
6-1 -31.400 -48.08413 -14.7158684 0.0002366
3-2 -5.825 -22.50913 10.8591316 0.8596397
4-2 -13.800 -30.48413 2.8841316 0.1358240
5-2 -16.250 -32.93413 0.4341316 0.0584142
6-2 -17.525 -34.20913 -0.8408684 0.0368627
4-3 -7.975 -24.65913 8.7091316 0.6384051
5-3 -10.425 -27.10913 6.2591316 0.3712401
6-3 -11.700 -28.38413 4.9841316 0.2612536
5-4 -2.450 -19.13413 14.2341316 0.9963066
6-4 -3.725 -20.40913 12.9591316 0.9756125
6-5 -1.275 -17.95913 15.4091316 0.9998411

$group2
diff lwr upr p adj
2-1 -2.083333 -14.167839 10.001173 0.9585513
3-1 -7.850000 -19.934506 4.234506 0.2804769
4-1 -0.250000 -12.334506 11.834506 0.9999203
3-2 -5.766667 -17.851173 6.317839 0.5325809
4-2 1.833333 -10.251173 13.917839 0.9710614
4-3 7.600000 -4.484506 19.684506 0.3057830

Since p-values for few pairs of group 1 are < 0.05, those pairs are signficantly diiferent at 5% level.
Pairs which differ significantly are : (23,75),(23,100),(23,125),(23,150),(50,150)

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