One possibility is  - Increasing the number of levels would indicate whether the relationship between the design (independent) and performance parameters is linear, quadratic, cubic etc or not.

When you create any type of designed experiment, you need to know the low and high settings for each factor you want to test. The number of levels are set by the user. If you have say 2 factors that are categorical, solvent and processing machine, then your levels for these factors are the solvents you use and the machines you can use.  

I prefer optimal designs over Taguchi. Taguchi designs force you to fit your experimental design to your experiment. Optimal designs allow you to fit your experiment to your design.So, if you have 6 factors, 2 are categorical and have 6 levels each, and 4 factors have 3 levels, (3-levels lets you see quadratic effects) you can get a design that fits your needs. Taguchi designs will force you to add an extra level to each categorical factor and possibly more levels to other factors.

A newer method for designing an experiment is using Definitive Screening Designs (DSD). These designs test 3 levels per continuous factor. If you have 2-level categorical factors, DSD can handle those too. 

If you have a good design of experiment program, I use Design Expert (DX) from Stat Ease, you can create many different types of designs, Optimal and DSD included.

Taguchi designs are good for what they were and in a pre-personal computer, pre-8-track world. Optimal Designs are old too but, they require a powerful personal computer to design. DSD are only a few years old and well received by industry.

Dear Adnan,

In Taguchi DoE, while designing experiments it is required to define input parameters and their levels. Here goal to determine the most significant parameter which affect the response of the process which to be analysed. Further, it is also needed to determine which level of that parameter is having significant effect on output response of the process. So that Optimum performance of process could be determined.

E.g. Suppose you are determining the effect of Depth of Cut, Feed rate and Spindle Speed on Material Removal Rate in Turning process. Then after Taguchi DOE analysis, it could be seen that Depth of Cut is most significant parameter affecting MRR. But while selecting levels one could analyse which level of DOC is having more influence on MRR. ie 1.5, 2, 2.5, 3, 3.5 etc.

You can read related reference material for better understanding. 

Dear Adnan

I used L9 with 3 factors & 3 levels with Taguchi confirmation test in my last work and I explain that step by step in my article. You can see my new publication in below link.

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Number of level of factor depend on the process knowledge.if your knowledge tells you that the relationship between response and factor is straight line linear; you can use 2 levels. If you are not so sure about the straight line relationship between response and factor;  you may have to increase to 3 levels to prove the relationship.

Please be gently reminded that   Intrinsic technology/knowledge comes first to guide the statistical technique.

I support Pricha's answer

For additional info.  In order to design the experiment by using Taguchi's method effectively.  The orthogonal arrays and linear graphs may be needed.  Reference  : TAGUCHI METHODS   ORTHOGONAL ARRAYS and LINEAR GRAPHS, Tools for Quality Engineering published by ASI Press in 1987is the excellent resource  for designing the experimental table.                             

Check this link out.

https://www.moresteam.com/toolbox/design-of-experiments.cfm#taguchi

Which *type* of Designed Experiment and the number of levels of the factors depends on the "nature" of the process you are investigating, and at what stage you are of the investigation . If you are early on (screening for important factors), you would use a screening type of Designed Experiment [e.g., Plackett-Burman, Fractional Factorial, Definitive Screening Design (DSD)]. If you know the important factors and want to move toward the optimum, you might use a Fractional or Full Factorial and then Gradient Ascent/Descent to move toward the optimum in a stepwise fashion (single run at a time). Once the optimum region is known, you could use a Response Surface Design (or in some cases a DSD even) to develop a Regression Model to fully quantify the region in terms of the important factors.

To wisely chose candidate factors, their ranges, and specific levels requires some process knowledge/experience. Choosing more than two levels for factors early on can be wasteful if those factors do not have a quadratic effect on the response in the region where you are starting. Generally, but not always, if you are not near the optimum, the (hyper)surface is not much "curved" and the factors will not (yet) have quadratic effects. But once you are in the optimum region some (all?) the factors will have quadratic effects.

I generally recommend being bold in setting the ranges the the factors, then choosing the levels at 20% and 80% of those ranges. Again, this decision is the domain of those with experience with the process. The drawback in setting the ranges too narrow is that some factors that are important may not show significant effects if their ranges are too narrow.

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I am thankful to all research scientist who shared their experiences regarding software for projection of anticipated results and use of experimental design work with projection of optimization model. Once you cannot find very determined output, Taguchi and Response Surface Method (RSM) might be a great help. Off-course you should know the lower and upper bond. In fact you should determine essential and effective process variable. The beauty of such software would be projection and interaction of variables in process optimization. I believe these software CCD and ... can be a great help for young scientist to conduct analysis of actual data. What we need justification of experimental data with projection model, that can easily be done by Taguchi or RSM.

Wish you all great success in your future research.

Videos of Taguchi Orthogonal array are available on this youtube channel.

you can take help from " Design of Experiments and Minitab " youtube channel