I would like to design an orthogonal array of trials for the Taguchi method. I have 4 independent variables, each having 5 levels. Therefore, the minimum no. of trials that are required come out to be 17. But in some research papers, I found that for similar requirements, people are going of L25 orthogonal array (i.e. 25 trials) instead of L17 array (17 trials). Does selecting a higher size orthogonal array offer some benefits?
Thanking you in anticipation.
Yes.it minimizes experimental error and improves accuracy of investigation.bt experimentation should be performed with more care.
Experimental error is not reduced by increasing the number of trials in an experiment. Confidence intervals will be narrower, but experimental error will usually be the same across all trials. I say "usually" because there are cases where the experimental error may change depending on different regions of the experimental space (typically due to measurement system sensitivity).
Also, more trials do not improve accuracy, rather they reduce uncertainty in estimates due to narrower confidence intervals. This is the property of precision, not accuracy.
If you are very confident that the optimum of the response space has been encompassed by the ranges independent variables and you wish to develop a regression model of the system, then 5 levels of the independent variables may make sense. I recommend 3 initially because 5 for some (or all) of the variables may not be necessary.
I will agree above valid points and it will increase experimental cost.
A full factorial (FD) will overwhelmingly identify all possible combinations in a given set of factors. Since, most of the clinical experimentation will usually involves a significant number of factors or attributes, a full factorial design (FD)resulted a large number of experiments, which can reduce the number of experimental parameters at practical level or essence , only a fewer number or small set observations was selected from the population (all the possibilities is being selected)The method of selecting a limited number of experiments which can produce the most cited information to the researcher , this newer method is known as partial fractional experiment (PFE). Since, this method is well known to see in Agricultural breeding trail or in house experiment,there are no general regularity guidelines for its own application or the analysis of the resulted findings.The data sets were obtained by experiment to performing the clinical experimentation. (Box et al. 1988 ) formulated a special set of general (modified ) design for conducting the research on full blown basis considering full factorial design (FD) that bears with too many applications or algorithms.
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