Determining number of samples per run in fractional factorial design

przem88

Hello everybody,

In one experiment we are going to measure 3d printed samples to improve prints quality (geometry). Additionally, I have value of standard deviation of sample run (10 samples distributed over printing bed, and printed under typical operation condition) to be 0.006mm and this should be standard deviation of measured geometry distorion. We want to minimize geometry distortion. We thought a fractional factorial design with 5 factors will be appropriate. Additionally I would like to use 4 central points. According to JMP I got table with 20 runs (minimum). I focused myself on main factors and 2-factor interactions. Without replicate runs I got, according to power analysis, power approx. 0.84. But how to determine the number of samples per run, to be possibly close to the real run mean? What needs to be considered?

I would appreciate for hints. If something is unclear I will try to explain.

Thank you

statman

"Data points" added to each treatment combination, while the treatment combination remains constant, are called repeats.  They are not independent events and do not add to the DF's for the experiment.  They can be quite useful.  The reason there is variation in the repeated data points cannot be due to the treatments as they are constant when the repeated measures are taken.  So the variation in those data points is likely due to short-term noise.  What noise is captured in those data points depends on how the data points are acquired.  For example, if the multiple measures are the same geometrical dimension at the same location on the printed part, then that variation is attributed to measurement error (e.g., measurement component of variation).  If the measures are the same geometrical dimension at different locations on the same printed part, then the variation in those data points would be indicative of both measurement error and within part variation.  If the data points are collected from various locations within the printing bed, then you can add the within bed component of variation to the potential source of that variation.  How many data points you need to estimate the variation of each component you want to include in your study is not a statistical question.  It is a function of how many measures will you need to represent the sources of variation you want to estimate.  How likely will the potential x's vary as you collect data?For example, if you are interested in understanding what factors effect within bed variation, how many locations would you want in the study to expose those effects?  The more specific your hypotheses, the more efficient your sampling.  Let's say, for example, you have an hypothesis that suggests how level the bed is will affect the dimensions.  So you chose locations on the bed that will expose that potential effect (probably locations at extremes of the printed part).