Determination of the effects for capacitor lifetime with Six Sigma DoE

Electrolytic capacitors are being used in almost all of the electronic circuits and maybe one of the most important "lifetime limiting" components [1] of these systems. With this study, we show a Six Sigma Design of Experiment (DoE) approach for determining the effect percentages of the potential factors on the lifetime of liquid electrolytic capacitors as a Six Sigma Black Belt Project. For the Six Sigma DoE; temperature, rated DC capacitor voltage, applied DC voltage percentage to the rated DC capacitor voltage (i.e., voltage derating factor) and the capacitance value were specified as experiment factors. Capacitor brands were specified as the experiment blocks and specified ripple current, specified Equivalent Series Resistance (ESR) value and the capacitor surface areas were selected as experiment covariates. As a result, a full factorial experiment system including 4 factors, 5 blocks, 3 covariates and center points was designed. The dependent variable in this experimental design was capacitance measured after 1000 hours. After running the 105 tests for 1000 hours, the final capacitance degradation values obtained at the end of the experiments were analyzed using the DOE tool of the Minitab software. First it was found that the center points have no statistical effect (P-value=0.541) on the experiment system. This means there was not a curvature in the response surface. Also the blocks do not have effect on the system as they had P-values in the range of 0.20 to 0.86 (P-value >>0.05). The P-value determines the appropriateness of rejecting the null hypothesis in a hypothesis test. P-values range from 0 to 1. The p-value is the probability of obtaining a test statistic that is at least as extreme as the calculated value if the null hypothesis is true. Before conducting any analyses, the alpha level is determined. A commonly used value is 0.05. If the p-value of a test statistic is less than the alpha, the null hypothesis is rejected [3]. The simplification of the experiment system was continued by dropping factors and their interactions having P-value > 0.05. After all the simplifications, the resulting table (Figure 2) was obtained where there remain no factors or interactions having P-value > 0.05. According to the results of the DoE, following outputs were obtained: To obtain the maximum capacitance degradation percentage, the temperature and the capacitance value must be high and the rated DC capacitor voltage must be low. The pie chart in Figure 5 shows the effect percentages of the factors on the capacitance degradation. The DoE gave the result that blocks (meaning capacitor manufacturers) have no effect on the designed system. To make comparison of the blocks, an ANOVA study was made. According to the results, the P-value = 0.428 (P-value >> 0.05), it cannot be said that "there is difference between the performances of the brands from the statistical point of view". This means that the results obtained in this study can be generalized (independent from the brand name). This work shows that control of the temperature and related capacitor attributes is the most important thing a designer can do to improve the lifetime of electrolytic capacitors.