This blog entry describes the application of the Taguchi design of experiments technique to .45 ACP load development in a Smith and Wesson Model 25 revolver.
Taguchi testing is an ANOVA-based approach that allows evaluating the impact of several variables simultaneously while minimizing sample size. This is a powerful technique because it allows identifying which factors are statistically significant and which are not. We are interested in both from the perspective of their influence on an output parameter of concern.
Both categories of factors are good things to know. If we know which factors are significant, we can control them to achieve a desired output. If we know which factors are not significant, it means they require less control (thereby offering cost reduction opportunities).
The output parameter of concern in this experiment is accuracy. When performing a Taguchi test, the output parameter must be quantifiable, and this experiment provides this by measuring group size. The input factors under evaluation include propellant type, propellant charge, primer type, bullet weight, brass type, bullet seating depth, and bullet crimp. These factors were arranged in a standard Taguchi L8 orthogonal array as shown below (along with the results):
As the above table shows, three sets of data were collected. We tested each load configuration three times (Groups A, B, and C) and we measured the group size for each 3-shot group.
After accomplishing the above, we prepared the standard Taguchi ANOVA evaluation to assess which of the above input factors most influenced accuracy:
The above results suggest that crimp (or lack thereof) has the greatest effect on accuracy. The results indicate that rounds with no crimp are more accurate than rounds with the bullet crimped.
We can’t simply stop here, though. We have to assess if the results are statistically significant. Doing so requires performing an ANOVA on the crimp versus no crimp results. Using Excel’s data analysis feature (the f-test for two samples) on the crimp-vs-no-crimp results shows the following:
Since the calculated f-ratio (3.817) does not exceed the critical f-ratio (5.391), we cannot conclude that the findings are statistically significant at the 90% confidence level. If we allow a lower confidence level (80%), the results are statistically significant, but we usually would like at least a 90% confidence level for such conclusions.
So what does all the above mean? Here are our conclusions from this experiment:
- This particular revolver shoots any of the loads tested extremely well. Many of the groups (all fired at a range of 50 feet) were well under an inch.
- Shooter error (i.e., inaccuracies resulting from the shooter’s unsteadiness) overpowers any of the factors evaluated in this experiment.
Although the test shows that the results are not statistically significant, this is good information to know. What it means is that any of the test loads can be used with good accuracy (as stated above, this revolver is accurate with any of the loads tested). It suggests (but does not confirm to a 90% confidence level) that absence of a bullet crimp will result in greater accuracy.
The parallels to design and process challenges are obvious. We can use the Taguchi technique to identify which factors are critical so that we can control them to achieve desired product or process performance requirements. As significantly, Taguchi testing also shows which factors are not critical. Knowing this offers cost reduction opportunities because we can relax tolerances, controls, and other considerations in these areas without influencing product or process performance.
If you’d like to learn more about Taguchi testing and how it can be applied to your products or processes, please consider purchasing Quality Management for the Technology Sector, a book that includes a detailed discussion of this fascinating technology.
And if you’d like a more in depth exposure to these technologies, please contact us for a workshop tailored to your needs.