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Engineering Science in
Additive Manufacturing Experimental statistics in AM

then fit single-factor polynomial trends to each factor and papers perform either a regression analysis, an ANOVA or
effect after the ANOVA, and they utilized contour plots both. Rarely are more advanced analyses performed, such
across different response variables to find samples which as Bayesian statistics and GLM. This means that only half
minimize all defects. Tables 1 and 2 depict how one can of the sampled papers use analyses that would quantify
efficiently report an experimental design and how to report the confidence that they had in their results. It is also not
the results of an ANOVA, respectively. clear if the other half of the papers even used appropriate
Tyagi et al., like Flores Ituarte et al., are interested in statistics. Very few papers performed model adequacy
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determining factors that significantly influence features of checks or used model selection techniques to find the best
tensile bars, such as tensile and compressive strength. This model. More worrisome, the sample points drawn in an
work used Taguchi’s L27 design and performed an ANOVA experiment may also not be independent of one another
on the results. Interestingly, they only investigated the due to the lack of randomization. This can have severe
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main effects of the model, even though they could have consequences, as an improperly randomized experiment
used a second-order model, but their analysis seems can conflate lurking variables with treatment effects and
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appropriate for their research questions. The authors also can introduce bias. Furthermore, extraneous sources
presented the appropriate ANOVA table and reported of variation are often not accounted for with experimental
their design matrix along with raw results. One major blocking, and the sample sizes used may not have been
issue is that some of their analyses were conducted using properly determined considering the appropriate signal-
signal-to-noise ratios, but without elaboration on why they to-noise ratio. This is not to suggest that these practices
were utilized. In his work, Taguchi defined several signal- were not performed, but rather that, at best, they were
to-noise ratios, but it is not clear which of these (if any) not reported. Therefore, our estimate for the frequency of
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the authors used in the study. these practices is likely an underestimate. However, this
still represents a problem, as the important aspects of the
While each of these papers generally used DOE design need to be reported so that the audience has the
effectively, there is still an opportunity for growth. tools to replicate the reported results. Another potential
Specifically, authors should report whether they checked source of bias stems from the fact that all of the studies
assumptions of their models, and why a specific statistical reviewed originate from academia; private companies
model was selected. In addition, sequential experiments can rarely disclose their experimental practices, even in patent
be performed, and a diverse range of models and designs filings, meaning that our analysis cannot capture the design
not used in these papers are available. By elucidating the and statistical approaches being used in industrial settings.
relevant literature, we aim to simplify the selection process
of appropriate models and designs for use in PBF-LB/M In addition, the field appears to be stagnant with regard
experiments. to the use of more sophisticated experimental techniques,
as the usage of useful RSM and screening designs has not
4. Concluding remarks changed over recent years. This finding was validated by
our cluster analysis, where we found that for both AM
4.1. Current practices and limitations and PBF-LB/M, all the manuscripts tend to cluster into
AM is a complex technical field, where the variance in the two broad categories: Those that use RSM as well as other
response of an experiment may be introduced in many steps standard experimental practices, such as randomization,
of the process. This variance should be minimized by the and those that utilize some of these practices but tend to
experimental design and/or accounted for in the statistical perform experiments poorly. We found that participation
model. While a few studies in the field demonstrate good in these clusters did not change over time for PBF-LB/M,
practice in this area, most of the sampled manuscripts did and in fact, in all AM, participation in the latter cluster
not explicitly justify their choice of experimental design is increasing with time, highlighting an urgent need to
in terms of minimizing the effect of inherent variance on improve the nature of the experiments in the field.
the results. Unfortunately, based on the papers reviewed,
this situation is not improving with time, or at least 4.2. Recommendations and future directions
not improving significantly. We also conclude that the Unlike traditional methods that generally shape pre-
experimental practices of PBF-LB/M do not differ from existing materials, AM builds both the material and
AM at large. However, neither field in general utilizes the geometry simultaneously. This “material creation in situ”
most accepted standard best practices of DOE. About half greatly increases the likelihood that a part can be used
of the sampled papers do not perform any statistics beyond immediately after the build, which, in turn, elevates the
just summarizing aspects of their data, such as the mean importance of rigorous statistical processes to guarantee
response (descriptive statistics). Most of the remaining consistency, reliability, and performance in end-use

Volume 1 Issue 4 (2025) 12 doi: 10.36922/ESAM025340021