Case Study 2: Electrostatic Powder Coating Process Optimization
(This case study is intended only to demonstrate general steps involved in experiment DESIGN and ANALYSIS tasks.Qualitek-4 (DOS) software was used for all design and analysis output which are best viewed by Netscape browser)
From the customer complaints and review of the production rejects, lack of uniform POWDER THICKNESS, VOIDS, and BRIDGING were considered major product
deficiencies. Powder/Coating Thickness among them was of primary concern and was considered as the single objective of the current study. The coating thicknesses obtained in current process range between .3 to .2 Mil(1/1000 inch). A consistent higher thickness (QC=BIGGER IS BETTER) was desired.
An L-8 orthogonal array with seven 2-level columns was used for the experiment design. The location of factors (columns 1, 2, 4, 5 and 7) and the columns reserved for the two interactions (columns 3 and 6) are as indicated in the table above.
The three noise factors were assigned two levels each and were incorporated in the study by an L-4 outer array. The outer array dictated that at least four separate samples be tested in each trial condition exposing them to the combinations of the noise factors as prescribed by the design. (The trial condition obtained by combining the control factors and the noise conditions from the noise
factors are not shown here)
One sample in each combination of the noise was tested under each trial condition. This meant that there were four samples tested in each of the trial conditions. The results from each sample and the Signal to Noise Ratios (S/N) for each trial results, are as shown below. As there are multiple results in each trial condition, analysis using S/N ratios was performed.
In S/N analysis, all calculations are made using the single column of trial S/N values. Thus, all numbers shown under Main Effect, ANOVA, and Optimum condition represent values in terms of S/N ratios. Also, regardless of the quality characteristics of the original evaluation (in this case Bigger is Better), bigger value, that is QC=Bigger, would always be the quality characteristic when carrying out S/N analysis.
The average column effects of the control factors and the interactions included in the study, are as shown below. Notice that, because there were two columns reserved for interactions, their influence in relation to the influences of the other control factors, are shown directly here as well as in the ANOVA (later). Whether any interaction columns is reserved or not, the presence of interactions between all possible factor combinations, however, can always be calculated (see case study 1, standard Qualitek-4 option). But, because PRESENCE does not necessarily mean SIGNIFICANCE, it is necessary to sacrifice columns for suspected interactions as their significance can only be studied when they appear in the ANOVA.
No matter which way the analysis is performed (S/N in this case), the average effects of the noise factors are always calculated in terms of the original units of measurements. The noise factor effects calculated below are all in terms of the measured coating thickness (Mil).
ANOVA of the control factor and the interactions included, indicates their relative influences (right most column) to the variations of the results. To minimize the chance of identifying something while it is not, it is a common practice to revise ANOVA by pooling insignificant factors. The revised ANOVA after pooling the two insignificant (done by comparing the confidence level with the desired value) factors are as shown below.
The performance at the optimum condition is estimated by considering only the significant factors and interactions. Since the analysis was performed using the trial S/N ratios, the estimated value represent the S/N ratio expected from a set of samples tested at the optimum condition.
Optimum condition shown above is determined from the main effects calculated above. But because there are significant interactions, the levels of interacting factors are adjusted by examining the test of presence of interaction plots.
The optimum factor levels are: Voltage (level 2), Air Box Pressure (level 1), and Brushing RPM (level 1). Review of interaction between Air Box pressure and Brushing RPM indicates (shown below) that the desirable level combination is level 1 for Air Box and level 2 for Brushing(X1,Y2). This means that the level of Brushing needs to be set to level 2.
Similarly, review of the interaction plot between factors Voltage and Air Box shows that level 2 of Voltage and level 1 of Air Box(X2, Y1 shown below for Bigger S/N), which are same as originally selected from the main effects, remain unchanged.
The corrected optimum factor levels are therefore are: Voltage (level 2), Air Box Pressure (level 1), and Brushing RPM (level 2).
There is no need to recalculate the expected performance at the optimum performance as it already includes the effect of significant interactions as shown in the optimum screen above.
Yopt = - 10.9008 in terms of S/N, which can be back-transformed to Y (expected) = .285 (in original units)
The expected performance is also expressed with Confidence Interval (C.I.) at 80% confidence level as:
Lower limit... S/N = -11.284 ( 0.273 in the original units of measurement)
Mean Value.. S/N = -10.9008 ( 0.285 in the original units of measurement)
Upper limit... S/N = -10.517 ( 0.298 in the original units of measurement)
SUMMARY OBSERVATIONS AND CONCLUSIONS
Significant Factors in Order of Influence:
EXPECTED SAVINGS: Savings = 40.97% (*)
* Savings(%) represents the percentage of $ loss at the current performance level. Thus if the current loss (based on average performance) is $1, then the savings expected is 40 cents.
Savings in dollars can be calculated from Taguchi Loss Function, L = K (MSD) for multiple parts. MSD can be calculated when S/N ratio is known. Lack of current performance status (in terms of S/N), the savings in relation to loss at the average performance (average S/N of all trials) can be calculated using the formula shown below. The savings calculation used these data: Improved design, (S/N)2 = -10.9008, condition represented by
average performance, (S/N)1 = -13.1900.
Savings = 1 - 10^(-13.1900 + 10.9008)/10 = 1 - .5903 = .4097 or 40.97%
Since MSD, S/N ratio, average, and standard deviations are all related, it is possible to draw the expected distribution and also calculate the increase of performance capability (Cpk).