Page 9 - ESAM-1-4

Engineering Science in
Additive Manufacturing Experimental statistics in AM

identifying key factors influencing product reliability and fitted model, where residuals are the difference between
enabling informed decision-making based on data-driven the model prediction of a data point and its true value.
insights. This paper aims to highlight essential statistical These tables and companion manuscript are the result of
techniques beneficial to the AM community, facilitating an extensive literature search of statistical manuscripts
the adoption of best practices and improving confidence and were produced in conversations with different AM
in AM-produced parts (for detailed discussions of specific experts. The designs are presented from the simplest to the
techniques). 26 most complex. Our underlying expectation is that as the

Statistics is a larger field than can possibly be covered statistical sophistication of AM advances, more complex
here, but this broad overview highlights some of the designs will be used.
minimum standards that should be applied to any While there is no unique recipe for conducting
experimental field. In this section, we introduce various experimentation, the steps depicted in Figure 1 provide a
experimental designs which can be used in different good blueprint for the proper application of experimental
contexts. We then present some of the good statistical statistics, regardless of the chosen experimental design.
practices that, in our opinion, are most relevant in AM. Most steps of this figure require further comment, and
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The set of basic designs we will cover are presented in reference should be consulted for further discussions of
Table 1, which includes a brief description of each design, these topics. It should be noted that there are many other
the conditions necessary for their proper implementation approaches, and other statisticians may change the order of
(whether or not a power analysis is needed to determine these steps or include other steps. In general, the steps consist
sample size, whether randomization is necessary, whether of the following: (1) Defining the problem, the population,
the underlying distribution needs to be checked, and and/or response variable of interest, and state hypotheses at
whether an experimental design matrix needs to be the onset to avoid introducing bias to the model selection
evaluated), and the section of the companion to this process. (2) Defining a statistical model (or set of models)
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manuscript in which they are discussed more thoroughly. based on the stated hypotheses. (3) Conducting pre-
Distribution checks are necessary to ensure that the experimental procedures to ensure experimental efficiency
data follow the assumptions of the model (i.e., analysis and trustworthiness of results. (4) Designing a sampling
of variance [ANOVA] assumes a normal distribution). strategy. Determine the number of samples needed, what
These checks can be done using different methodologies, types of measurements need to be made, and how bias
but the most common is to check the residuals of a can be avoided by performing appropriate sampling. (5)

Table 1. Overview of experimental techniques, associated statistical tests, and minimum reporting requirements
Technique Statistical test Minimum conditions Section
Sample size Random‑ization Distribution Design number in
determination check matrix ref. 26a
Simple hypothesis t-test ✓ ✓ ✓ 2.3, 3.2
testing
One-way design F-test ✓ ✓ ✓ 2.4, 3.3
One-way design with F-test ✓ ✓ ✓ 2.5
blocking
Split-plot one-way F-test ✓ ✓ ✓ 2.6
design
One-way nested F-test ✓ ✓ ✓ 2.7
design
Full factorial F-test combined with a first-order ✓ ✓ ✓ 2.8
regression model
Fractional factorial F-test combined with a first-order ✓ ✓ ✓ 2.9
regression model
Response surface F-test combined with a second-order ✓ ✓ ✓ 2.10
methodology (RSM) regression model
Sequential F-test combined with the first- and ✓ ✓ ✓ 2.11
experiments second-order regression model
Notes: Section number in reference which discusses each technique.
a
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Volume 1 Issue 4 (2025) 3 doi: 10.36922/ESAM025340021