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Contents • Factorial designs • Response surface methodology [ccd, historical design, optimization techniques]
Historical design • Response Surface Methodology (RSM) is a statistical experimental design technique used to study the relationship between a response variable and several predictor variables. In RSM, historical design is a type of design that is used when there is prior knowledge or historical data available about the factors and their levels. • Historical design involves using the existing knowledge about the factors and their levels to create a design matrix that can be used to conduct the experiment. • The design matrix is based on a statistical model that relates the response variable to the predictor variables, and it is created using software tools such as Design Expert or JMP
Steps in historical design • The steps involved in historical design in RSM are as follows: • Identify the response variable and predictor variables: The first step in historical design is to identify the response variable and predictor variables. The response variable is the variable that is being studied, while the predictor variables are the variables that are expected to have an effect on the response variable. • Identify the levels of the predictor variables: The next step is to identify the levels of the predictor variables based on prior knowledge or historical data. The levels should be chosen so that they cover the expected range of the predictor variables. • Determine the number of runs: Once the levels of the predictor variables have been identified, the next step is to determine the number of runs required for the experiment. The number of runs is determined by the statistical model and the degree of precision required. • Create the design matrix: Using the identified levels and the number of runs, a design matrix is created using software tools such as Design Expert or JMP. The design matrix specifies the combinations of the levels of the predictor variables that are to be used in the experiment. • Conduct the experiment: The experiment is conducted according to the design matrix, and the response variable is measured for each combination of predictor variable levels. • Analyze the data: Once the experiment is complete, the data is analyzed using statistical methods such as regression analysis. The statistical model is used to estimate the effects of the predictor variables on the response variable and to optimize the response variable based on the desired criteria. • In conclusion, historical design is a type of design in RSM that is used when there is prior knowledge or historical data available about the factors and their levels. The design matrix is created based on a statistical model that relates the response variable to the predictor variables, and the experiment is conducted according to the design matrix. The data is then analyzed using statistical methods to estimate the effects of the predictor variables on the response variable and to optimize the response variable based on the desired criteria.
Optimization techniques • There are several optimization techniques Steepest Descent: This is a gradient-based optimization technique used to identify the direction of the steepest slope in a response surface. The method involves starting at a point on the response surface and iteratively moving in the direction of the negative gradient until the minimum point is reached. Simplex Method: This is a popular optimization technique that uses geometric concepts to iteratively move towards the optimal solution. The method involves creating a simplex, which is a set of points that define the corners of a polytope. The simplex is moved in the direction of the minimum point until the optimal solution is reached. Gradient Search: This is another gradient-based optimization technique that involves calculating the partial derivatives of the response function with respect to each input variable. The method involves moving in the direction of the negative gradient until the minimum point is reached. Response Surface Methodology: This is a popular optimization technique that uses a response surface to model the relationship between the input variables and the response. The method involves fitting a second-order polynomial to the data and using the coefficients of the polynomial to identify the optimal solution. Evolutionary Algorithms: These are a class of optimization techniques that use the principles of evolution to identify the optimal solution. The method involves creating a population of potential solutions and using selection, mutation, and crossover to evolve the population towards the optimal solution
