Box Behnken Response Surface Methodology RSM Design and Analysis Example using Minitab & MS Excel

what is box back in design in response surface methodology in this video explain what is box back in design how to design it and also how to collect the data and how to analyze it using Minitab also in excel how to design it in excel as well so box back in design is a three level design for each factor in this example we have seen in the past we have used this example a lot the temperature humidity and I have added another factor the light level so let's say that the center point for the temperature

is 72 degree Fahrenheit is the optimum level comfort level for so at 72 degree people feel more comfortable and say we want to go 5 degree down from there and then 5 degree up setting the other two levels low level and high level for the humidity assume that 50% is the optimum and then we want to say 20% higher and 20% lower to get the other two levels to make the three levels now for the lighting level say for example 10,000 Lux is the amount of light that we need for that particular task done in

that room or whatever we are trying to do this study and then the we go 5,000 down and 5,000 up to set the level so this is basically in in the picture you can see here in this cube that this is a design with one center points and then twelve other points so let's go to excel and let me show you how you actually can design this this will give you a little bit more idea about what's going on behind the scene in Minitab so if you look at these this is the layout for a

three factors and three level for each factor design here we have these as you can see here a B let's say temperature and humidity this is a basic two square design if you know don't know how to do that you can go to the open air together comm slash do e take the factorial design which is the basics to the center basic to the response surface methodology so assume that you know how to create this twist square if not was the first video under the factorial design so you basically create these and then add a

center point for the third variable so it's very simple as you can see here this is a balanced incomplete design so a simple enough just type 0 0 center point for on this B and then set center point for a and for the center points you can collect maybe as low as 1 point or 3 if you have more than you have more degrees of freedom also you will be able to test the lack of feet but just to do the response surface one point is enough so this is how you design it and then

you go collect the data the response here let me go to Minitab and show you how to design it we need to have so what we start do e response surface create a design so send up composite is by default selected select box by again and then you can see the available design here it is start with the 3 factor there is no two factor box back in design so and then you can see basically leave everything default hit OK it will produce this design for you if you don't wanna do it in Excel now

once you design it and collect the data let's say you have all these levels and collect the comfort level from 15 subjects and then let's see how to analyze this in Minitab so the analysis is not really any different than the so once you've done the design selected Comfort heat okay it'll do the analysis for you as you can see here temperature the the linear levels are not really significant is the nonlinear term for both temperature and humidity are significant rest of the stuffs are not significant now pause this data in the open etiquette or

calm so you can see you can run the analysis by yourself to see now this data is generated by random numbers so it'll change a little bit I didn't keep the original one but the result will be very close so let me show you how to then create the response surface and contour plot so response surface basically everything is said there now you could choose the other one light here but light is not significant so not really interested in that so temperature and humidity and then comfort is a response heat okay so this will produce

the response surface for you a lot of time contour plot is easier to explain so let me go show you how to produce contour plot same thing basically as you can see here there is a range where you feel the most comfortable now the humidity lines are more parallel so as you go along with this y-axis or humidity axis there is not much significant difference in comfort however if you go along the x-axis you see lot of changes just a little change of temperature changes the comfort level so basically it's a simple way of doing

response surface using this box bacon design