Delete DoE.Rmd

DoE/DoE.Rmd

----
-title: "Design of Experiments"
-author: "El-hassane Nour"
-date: "January 8, 2023"
-output:
-  pdf_document: default
-  html_document: default
----
-
-```{r setup, include=FALSE}
-knitr::opts_chunk$set(echo = TRUE)
-```
-# Note:
-
-Since I couldn't install DoE.wrapper, I run the experiments online using this website [DoE.wrapper](https://rdrr.io/cran/DoE.wrapper/)
-
-# Playing with the DoE Shiny Application
-The model studied in this experiment is a black-blox, where x1, x2, ..., x11 are controlable factores, z1,...,z11 are uncontrolable factors and y is the output. 
-In order to approximate this unknown model, we need first to determine which variables are the most significant on the response y, using screening designs.
-
-Then, define and fit an analytical model of the response y as a function of the primary factors x using regression and lhs & optimal designs.
-
-## 1. First intuition
-My first intuition was to run an lhs design using the 11 factors to have a general overview about the response behavior. 
-```{r}
-library(DoE.wrapper)
- set.seed(45);
-design <- lhs.design(type= "maximin", nruns= 500 , nfactors= 11, digits=NULL, seed= 20523, factor.names=list(X1=c(0,1),X2=c(0,1),X3=c(0,1),X4=c(0,1),X5=c(0,1),X6=c(0,1),X7=c(0,1),X8=c(0,1),X9=c(0,1),X10=c(0,1),X11=c(0,1)))
-
-design.Dopt <- Dopt.design(30, data=design, nRepeat= 5, randomize= TRUE, seed=19573); design.Dopt
-```
-Once data was generated, I tested it on the DoE shiny app and got a csv file containing the generated data with the corresponding response.
-```{r}
-df <- read.csv("exp.csv",header = TRUE, colClasses=c("NULL", NA, NA, NA, NA, NA, NA, NA,NA, NA, NA, NA, NA));
-df
-```
-## 2. Designing experiments to run
-### 2.1 Screening design using Plackett-Burman screening designs
-Now, we're interested to see the factors effects in more in details. This will allow us to define the most efficient factor that influence the response. Since running a large number of such experiments is tedious, we gonna use the Plackett-Burman designs to see the different possible interactions.
-```{r}
-library(FrF2)
-d<-pb(nruns= 12 ,n12.taguchi= FALSE ,nfactors= 12 -1, ncenter= 0 , replications= 1 ,repeat.only= FALSE ,randomize= TRUE ,seed= 26654 ,factor.names=list( X1=c(0,1),X2=c(0,1),X3=c(0,1),X4=c(0,1),
-X5=c(0,1),X6=c(0,1),X7=c(0, 1),X8=c(0,1),X9=c(0,1),X10=c(0,1),
-X11=c(0,1)));d
-```
-
-Here are the results (run on the website):
-
-   X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
-1   1  0  1  1  0  1  1  1  0   0   0
-2   1  0  0  0  1  0  1  1  0   1   1
-3   0  0  1  0  1  1  0  1  1   1   0
-4   0  1  1  0  1  1  1  0  0   0   1
-5   0  1  0  1  1  0  1  1  1   0   0
-6   1  1  0  1  1  1  0  0  0   1   0
-7   1  1  1  0  0  0  1  0  1   1   0
-8   1  0  1  1  1  0  0  0  1   0   1
-9   0  0  0  0  0  0  0  0  0   0   0
-10  1  1  0  0  0  1  0  1  1   0   1
-11  0  0  0  1  0  1  1  0  1   1   1
-12  0  1  1  1  0  0  0  1  0   1   1
-
-### 2.2. Regression and Analyse of Variance
-In order to vizualise the correlation between factors and the response, we do a linear regression on the data generated by the application, and analyse the variance to see the effect.
-
-#### Experiment 1: X1, X3, X4, X6, X7, X8 taken into account
-```{r}
-y<-df$y
-summary(lm(y~df$x1+df$x3+df$x4+df$x6+df$x7+df$x8,data=df))
-```
-Nothing interesting :/, even R^2 is too small wich is too bad.
-
-#### Experiment 2: X1, X5, X7, X8, X10, X11 taken into account
-```{r}
-y<-df$y
-summary(lm(y~df$x1+df$x5+df$x7+df$x8+df$x10+df$x11,data=df))
-```
-Very small improvement in R^2, but still too bad.
-
-#### Experiment 3: X3, X5, X6, X8, X9, X10 taken into account
-```{r}
-y<-df$y
-summary(lm(y~df$x3+df$x5+df$x6+df$x8+df$x9+df$x10,data=df))
-```
-It seems that X9 is a significant factor that influences the model, and the determination coefficient R^2 is 0.73 now, which is pretty good.
-
-#### Try the combination X3*X6:
-```{r}
-y<-df$y
-summary(lm(y~df$x3+df$x9+df$x6+df$x3:df$x6,data=df))
-```
-
-Not too much interesting. Let's try another experiment where X9 and X3 are set to 1.
-
-#### Experiment 8: X1, X3, X4, X5, X6, X9, X11 taken into account
-```{r}
-y<-df$y
-summary(lm(y~df$x1+df$x3+df$x4+df$x5+df$x6+df$x9,data=df))
-```
-
-Removing X11 doesn't have any effect. We decide to keep X9, X6, X4, combine X5 with X7, combine X1 with X3.
-
-```{r}
-y<-df$y
-summary(lm(y~df$x3:df$x1+df$x6+df$x5:df$x7+df$x4+df$x9,data=df))
-```
-We can say that our model is:
-y= -2.72\*X9 + 0.72\*X4 + 0.42\*X6 + 0.99\*X1\*X3 -0.77\*X5\*X7 + 1.55
\ No newline at end of file