It is a statistical tool suggested by G Taguchi. L9 is an orthogonal array which can be used to conduct experiments involving typically 4 factors set at 3 levels.. in L9 it has 9 trials or runs that are recorded with each factor (process parameter) set at different level. Using the recorded data, S/N ratio (signal to noise) ratio is computed and Graphs are plotted to select the optimal factor level settings..
Taguchi design is one of the robust design techniques used in most manufacturing industries where many independent variables affect the output. It involves a minimal number of experiments. L9 orthogonal array is used to analyze 4 factors each at 3 levels with 9 experimental runs. The array assumes that there is no interaction effect between variables, only main effects are analyzed. It is used to determine the effect of each independent variable on the response/output by calculating signal-to-noise-ratio and variation is more interesting than average in the Taguchi method.
In relation to optimization, Response surface methodology (central composite design and Box-Behnken design) are preferable to Taguchi design (method).
In addition to the advice of other colleagues, in order to learn more details and detailed explanations, I suggest you read the books and articles whose links are given below:
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