For modern electronic products, a multidisciplinary, versatile and small design
ID: 3259913 • Letter: F
Question
For modern electronic products, a multidisciplinary, versatile and small design has become increasingly attractive in recent years. The circuitry on printed circuit boards (PCBs) is becoming extremely sophisticated. Furthermore, global competition calls for PCB manufacturers to improve overall performance. The quality of products and services is a reflection of company quality. Thus, excellent quality is an extremely crucial issue for PCB manufacturers. A Six Sigma project was implemented using the DMAIC roadmap at a PCB manufacturer. This company produces multi-layer PCB products and supplies computer manufacturers in China. Customers continually complained of exposed copper on annular rings of PCBs seriously affecting product yield rate. Due to the exposed copper on annular rings, solder was not absorbed between hole walls and annular rings, thereby generating vacuoles in the insertion process. A Six Sigma project was created that specifically focused on resolving the exposed copper problem. After a brainstorming session, the project team determined that the exposed copper on annular rings may result from unclean image development during the developing process. The ultimate goal of this Six Sigma project was to improve and control the performance of the developing process with seamless control plans while eliminating the problem of exposed copper on annular rings. An ANOVA is performed to eliminate exposed copper defects on annular rings of PCBs during the developing process. The four critical variables were considered in this study, including the dot pattern size on the stencil, the placement time after printing and temperature and humidity during placement, were then analyzed by applying the DOE method and a comparison test. The dot pattern size on the stencil and the placement time after printing were chosen as factors for implementing a two-factor DOE with two levels. The dot pattern size on the stencil had two levels: (1) 1.5 mm larger than the diameter on one side of a pad; and (2) 6 mm smaller than the diameter on one side of a pad. The levels of the placement time after printing were divided into 15 minutes and 80 minutes. Both temperature and humidity during the 9 placement period after printing were controlled within appropriate specifications. Each experiment was replicated twice, and percentage of the defective PCBs with exposed copper on annular rings was determined, as shown in the Table 1. The dot pattern size on the stencil and the placement time after printing were chosen as key point input variables. The ANOVA result is already provided in Table 2, where the significance level is set as 5%. Having confirmed the effects of the two key point input variables (KPIVs), the project team focused on environmental factors, including temperature and humidity before pre-curing. A comparison experiment was designed to observe the influence of these environmental factors prior to pre-curing. The dot pattern size on the stencil was set 6 mm smaller than the diameter on one side of a pad. Average temperature and humidity were controlled 1. What are the assumptions needed for conducting a DOE? (10 points) 2. Name the factors that were tested and list their levels. (10 points) 3. State the hypotheses that should be tested in this experiment. (10 points) 4. Explain the main effects plot and the interaction effects plot. (20 points) 5. Interpret the results of the comparison test. (10 points)as 22C and 55% in the first group, and 35C and 70% in the second group. The placement time after printing was set to 15 and 80 minutes. The comparison result is shown in Table 3.
Table 1. DOE Result Main Effects Plot (data means) for Defective % Factor 1 The dot pattern size on the stencil (mm) Factor 2 The placement time after printing (mins) The dot 12 Defective percentage (%) 0.01 6.2 0.17 18.72 15 80 5.6 0.3 16.9 Table 2, ANOVA for Defective PCBs (%) 15 DF Seq SS Adj SS Adj MS Significance Figure 2. Main Effects Plot for Defective 2 349.110 349.110 174.555 378.50 0.000 Main effects 2-way interactions 1 Residual error Pure error Total 68.2 68.2 68.211 147.90 0.000 1.845 1.845 7 419.166 1.845 1.845 0.461 0.461 Interaction Plot (data means) for Defective % 4 6.0 L.5 Table 3. Comparison Test Group 1 Average temperature: 23 C; Average humidity: 55% Group 2 Average temperature: 35°C; Average humidity: 70% Placement time (min) 15 206 Placement time (min) xperiment 15 40 80 Experiment 2 40 80 175 21 12.00% 224 95 42.41% ample 24 268 Sample 0 Defect fect fective percentage 15 0% 1.24% 0% Defective 2.43% The placement time percentage Figure 3. Interaction Plot for DefectiveExplanation / Answer
The dot pattern size on the stencil and the placement time after printing were chosen as factors for implementing a two-factor DOE with two levels. The dot pattern size on the stencil had two levels: (1) 1.5 mm larger than the diameter on one side of a pad; and (2) 6 mm smaller than the diameter on one side of a pad.
1. What are the assumptions needed for conducting a DOE?
Assumptions :
2. Name the factors that were tested and list their levels.
The two factors are dot pattern size on the stencil and placement time after printing.
The levels of the placement time after printing were divided into 15 minutes and 80 minutes. Both temperature and humidity during the 9 placement period after printing were controlled within appropriate specifications.
3. State the hypotheses that should be tested in this experiment.
Here we have to test the hypothesis that,
H0 : Fator dot pattern size on the stencil is insignificant.
H1 : Fator dot pattern size on the stencil is significant.
H0 : placement time after printing is insignificant variable.
H1 : placement time after printing is significant variable.
H0 : There is no interaction between dot pattern size on the stencil and placement time after printing.
H1 : There is interaction between dot pattern size on the stencil and placement time after printing.
Assume alpha = level of significance = 0.05
Here for all the hypothesis the test statistic follows F-distribution.
We see that,
Test statistic (Main effect) = 378.50
P-value = 0.000
Test statistic (two way interaction) = 147.90
P-value = 0.000
We see that P-value < alpha
Reject H0 at 5% level of significance.
Conclusion :
Fator dot pattern size on the stencil is significant.
placement time after printing is significant variable.
There is interaction between dot pattern size on the stencil and placement time after printing.
4. Explain the main effects plot and the interaction effects plot.
From the plot also we can see that main effect and interaction effects are significant.
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