Since the experimental data and design vectors were previously entered into
an electronic spreadsheet, it was possible for the team to further explore the
data via systematic sorting and stratification. The team required an entire
day planning the flow of analysis. (Although this may initially seem
excessive, it is easy to get lost exploring the many trivial analytical
tributaries that periodically result from the data. To avoid this pitfall, a
plan of attack must be carefully developed in light of realistic objectives
and then adhered to. This is not to say that the tributaries be avoided
because they often yield valuable information: however, the data analysis must
be planned prior to executing the experiment.)
In accordance to plan, the first activity involved sorting the entire experimental matrix and related row-wise response measures by design vector. This had the advantage of separating the positive design vectors of any given column factor from its negative design vectors.
Next, the data was stratified by quadrant, coupon, subquadrant, hole, etc. so the data could be plotted by line number. The many resultant graphs provided a basis from which to visualize the main effects and potential interactions at various analytical and product strata.
By following this strategy, the team was able to assess the consistency of effects across the intelligent area of each board as well as the related coupons. This extremely important point means that if the experimental effects were not consistent, it would have been highly likely that the problem could have been resolved in one portion of the PCB or rack and subsequently magnified in some other area, thereby neutralizing the gains. Even worse, it might have been possible to narrow the range of variability within a certain board location, but throw the mean far off target in some other location. Recall that the purpose of experimentation was to reduce the variance without impacting overall mean location.
Figure B-30 and Figure B-31 illustrate the sequential plot of standard
deviations associated with the two most important main effects - factors G and
H. The horizontal axis of this graph was tied to the spreadsheet line number
and the vertical axis reflected the corresponding standard deviation. This
way, the data could be sorted in any given fashion and subsequently plotted in
a manner such that the negative design vectors graphically appear before the
positive vectors. Line markers 1 through 8 within Figure B-30 display the
standard deviations when factor G was set at its low test level. Line markers
9 through 16 illustrate the behavior of the standard deviation when factor G
was at its high test level. From this graph, it is apparent that when factor G
was held at its low test level, the response standard deviation was smaller on
the average, than when the high test level was considered.
In the context of the experimental objectives, the smaller standard
deviation was more desirable. It is also apparent that factor G interacts with
some other factor because the response standard deviation was more stable at
the low test level than at the high test level. This was confirmed when the
ANOVA tables were individually considered together with several other
Based on the experimental outcomes, realistic tolerances and/or operating conditions were established for factors B, G, and H.
NOTE: It is beyond the scope of this particular case study to present the outcomes of the entire data analysis. Only a small portion of the total analytical picture is presented. The most important concept to be gained is an understanding of the analytical strategy and approach, not the physics associated with plating PCB through-holes.
The reader is cautioned not to attempt
replication of this experiment on the basis of the information given in this
case study as the data is incomplete. The strategy, tactics, and tools can
be replicated, but the data cannot be used "as is" to make improvements
within an existing process - the outcomes are unique to the XYZ