# Statistical Analysis of Leakage Data

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The data for this report was taken from the journal Quality Engineering and the name of the article was "Sequence-Leveled Experimental Designs at Work" written by C.W. Carter and T.B. Tripp. The data observed was aimed at determining the significant factors affecting the leakage of tantalum capacitors. Data table 6 from the article was used in this statistical project. The data table was broken down into eight columns. It was first observed at both 60Ñ"C and 80Ñ"C. Also for each of the degrees it was taken when it was 50V and 125V through the capacitor. Further it was measure at each of the voltages at 0 ppm and 80ppm. From this data it was the objective of the project to use the Minitab program ANOVA to determine if all the factors were necessary in determining the solution. After determining whether or not there were unnecessary factors the procedure was then done again. In this case we found that the Voltage would be disregarded because it was greater then the alpha that we chose, which was .05 using the P-value test. The test was continued and it was found that the other factors were indeed significant. A t-test statistic was also preformed to determine whether or not to reject the null hypothesis, using the data specifically from the ppm data. Due to the results it was observed that the null hypothesis should be rejected. Further more the data was then tested to using a normal probability plot to determine if the data was normal.

ANOVA on the Minitab program proved to be the best method of determining which factors would be significant. To figure this out, the numbers from the data were placed into one single column and then the three factors were placed in three different columns using the ANOVA methods. The following shows the results of ANOVA and what was concluded from it.

General Linear Model: C1 versus ppm, V, C

Factor Type Levels Values

ppm fixed 2 1 2

V fixed 2 1 2

C fixed 2 1 2

Analysis of Variance for C1, using Adjusted SS for Tests

ppm 1 123362778 123362778 123362778 27.13 0.000

V 1 12200977 12200977 12200977 2.68 0.106

C 1 110873422 110873422 110873422 24.38 0.000

Error 68 309244305 309244305 4547710

Total 71 555681482

Unusual Observations for C1

Obs C1 Fit SE Fit Residual St Resid

11 16500.0 4450.2 502.6 12049.8 5.81R

15 9370.0 4450.2 502.6 4919.8 2.37R

R denotes an observation with a large standardized residual.

Using alpha to be .05, we had the three factors (ppm, V, C) to be the possibilities. Looking at the results, the voltage factor was not significant and did not effect the result since it was greater then the alpha used in the test.

Looking at the data set 11 and 15, one can conclude that the two points are out of line with the others since the residuals for those points are significantly large.

General Linear Model: C1 versus ppm, C

Factor Type Levels Values

ppm fixed 2 1 2

C fixed 2 1 2

Analysis of Variance for C1, using Adjusted SS for Tests

ppm 1 123362778 123362778 123362778 26.48 0.000

C 1 110873422 110873422 110873422 23.80 0.000

Error 69 321445281 321445281 4658627

Total 71 555681482

Unusual Observations for C1

Obs C1 Fit SE Fit Residual St Resid

11 16500.0 4038.6 440.6 12461.4 5.90R

15 9370.0 4038.6 440.6 5331.4 2.52R

R denotes an observation with a large standardized residual.

Since the first test concluded that the factor V was insignificant, we just wanted to make sure that the other two factors ppm and C were significant. Since after doing the ANOVA test with ppm and C as the two possibilities, we notice that the P value is 0, which means that V is definitely not significant and the other two are.

General Linear Model: C1 versus ppm, V, C

Factor Type Levels Values

ppm fixed 2 1 2

V fixed 2 1 2

C fixed 2 1 2

Analysis of Variance for C1, using Adjusted SS for Tests