Experiments 5E - RSM in 2 factors: introducing the case study

[@satyakrishnacookingchannel6908]

Sir, Thank you for the videos. if I want to use only temperature and time( two factors) as independent variables and heating value as a response: in this case how we can explain the experimental advantages of DOE over OFAT. It is requested to kindly give me a reply.

[@quanghuytran7418]

Thank you for your online book, so interesting!!!

[@abdulraziqhakimi635]

tnx for useful videos, great explanation!!!

[@KevinDunn13]

Glad to hear that Abdul!

[@do0oma]

Thanks a lot for this wonderful video and smooth explanation... I was just wondering how to set the actual values in relation to the coded values of the levels (-1.41,-1,0,1,1.41)?? For example if my factor is treatment time(from 0min "low=-1" to 5min "high=1", and I would like to run a face centred design, could I relate the 0 level to 1min treatment time? or should it be exactly in the middle of both low and high values (2.5min in that case)?? Please advise

[@KevinDunn13]

Hi Adham: great question! In your example the 0 point would indeed be at 2.5 minutes. You can watch some of the other videos in this playlist (particularly 5A, 5B, 5C and 5D) to get a sense of that. These videos actually make part of a free course on Coursera: www.coursera.org/learn/experimentation where you can get more than just these videos.

[@do0oma]

Thanks a lot for your quick response.. I found the answer to my question in the formula provided in this video, I asked too quickly before coming to that point in your video (I appologize). But I was also wondering if it would be a good idea to start my experimentation jumping directly to a face centred design using a broad range of levels (0min to 5min treatment time), just to get a general idea of the response, and narrow down my levelling spectrum afterwards in my next experiment in the high response region (choosing my new levels to 2.5min and 3.5min for example)?? Because in my case, although 0min and 5min are the constrains of operation, I doubt if narrower levels would have any effect on the response. And I have to mention that I really gained a lot of knowledge, in the smoothest way, watching this outstanding course... Thanks a lot for your efforts and dedication. I appreciate it :)

[@KevinDunn13]

If the experiments don't cost much time or money, then it is okay. Generally the advice is to start with a simple factorial cube. Since you don't know if you are far from the optimum or close by. If you are far away, then the extra experiments from the face add no real value, other than confirmation. Once you are closer to the optimum (tips in the video tell how you might know that), then you want to bring the size of the cube in (to avoid stepping too broadly past the optimum) and to add those face centered points, and points that will support quadratic models (the +/- 1.41 points). Since by definition an optimum will be nonlinear, you will need those nonlinear terms at/near the optimum. The video 5B lays out those ideas, except for a optimum in terms of a single variable, or factor. But the principle for multiple factors is the same. Further, I wouldn't recommend starting your experiments at the constraints (0 and 5 min), since you will almost certainly span a nonlinear region, and try to fit that with a linear model. Start much smaller: around 2.5 at the center, with +/- 1 minute, would be my advice, in the absence of knowing more about your system.

[@do0oma]

Kevin Dunn Thanks a lot for your valuable advise... I will come back to the videos you recommended... you are saving me a huge time and effort going through some complicated statistical text books to get such valuable knowledge... I appreciate it

[@do0oma]

Another question please. In case of examining the effects of 3 levels for an experiment with 2 factors. If, for practical reasons, it would be favorable to choose the mid level not exactly in the middle of the high and low levels, and in case I would choose 2.5 min treatment at the center as you kindly suggested, would it be possible to formulate a nonlinear model while choosing the low level at 2 min treatment and the high level at4 min treatment? would this mean that I have to change the corresponding coded values of the high and low to a fractional values instead of the integers -1 and 1? Please advise. Thanks again for your continuous support :)

[@kpoplove9819]

Is this model applicable in problem having 3 levels high medium low?

[@KevinDunn13]

Absolutely. you can code low as -1, medium as 0 and high as +1, provided they are indeed equally spaced.

[@angelinamiller3306]

when you have curves instead a linear surface, and you want to minimize, but for it, you have 2 options in 2 directions, but if you wanted to maximize you'd have a clear direction (diferent to before ones and not opposite to before ones)??

[@KevinDunn13]

Hi Angelina, one way to answer your question is to realize that any optimum (maximum, or a minimum) will come to a point. No matter how you approach it, there will be a clear direction. What you are describing might be what you see as you are on the path towards a minimum. In that case, the general rule is to take the path that is steepest descent (minimum) or ascent (maximum). However, in practice we have extra knowledge about our systems, and we can choose any path we like, as long as we head in the general direction. Remember, the goal is to get there, and it might mean to take an extra step or two along the way, especially if each experiment is not too costly. Kevin