The response surface methodology (RSM) is a collection of mathematical and statistical techniques for the construction of empirical models. By carefully designing the experiments, the goal is to optimize a response (output variable) that is influenced by several independent variables (input variables). An experiment is a series of tests, called runs, in which changes are made to the input variables to identify the reasons for the changes in the output response.
In statistics, the response surface methodology (RSM) explores the relationships between various explanatory variables and one or more response variables. The method was introduced by George Box and KB Wilson in 1951. The main idea of RSM is to use a sequence of experiments designed to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They recognize that this model is only an approximation, but they use it because it is easy to estimate and apply, even when little is known about the process.
Statistical approaches such as RSM can be used to maximize the production of a special substance by optimizing operating factors. Unlike conventional methods, the interaction between the process variables can be determined using statistical techniques.
Summary
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- 1 Basic approach to response surface methodology
- 2 Practical applications
- 3 Practical concerns
- 4 Source
Basic approach to response surface methodology
An easy way to estimate a first-degree polynomial model is to use a factorial experiment or a fractional factorial design. This is sufficient to determine which explanatory variables affect the response variables of interest. Once only significant explanatory variables are suspected to remain, a more complex design can be implemented, such as a central composite design to estimate a second-degree polynomial model, which remains only an approximation at best. However, the second grade model can be used to optimize (maximize, minimize, or achieve a specific goal for).
Practical applications
As tool Lean Six Sigma , RSM can be used in the sugar harvest of Cuba as a method to be more efficient. For example, reducing the moisture content of sugar bagasse . Since most of the bagasse is finally burned in the boilers to generate steam, a reduction in the humidity of the bagasse results in an increase in the efficiency of the boiler and consequently a reduction in the consumption of bagasse for a given steam production.
Suppose that the moisture content depends on 4 factors: Brix juice, imbibition, sucrose content, and mill speed. In this case, the objective is to minimize humidity (output variable) which is influenced by 4 independent variables (input variables).
In the case of humidity optimization, the engineer wants to find the levels of (x1, x2, x3, x4) that minimize the humidity (y) of the bagasse. The function of the levels and humidity is as follows: y = f (x1, x2, x3, x4) + ε where ε represents the noise or error observed in the response y. The surface represented by f (x1, x2, x3, x4) is called the response surface.
Practical concerns
The response surface methodology uses statistical models, and therefore, professionals should be aware that even the best statistical model is an approximation to reality. In practice, both the models and the parameter values are unknown and subject to uncertainty in addition to ignorance. Of course, an estimated optimal point does not actually need to be optimal, due to estimation errors and model weaknesses.
However, the response surface methodology has an effective track record of helping researchers improve products and services: for example, Box’s original response surface modeling allowed chemical engineers to improve a process that had been stuck for years in a saddle. The engineers had been unable to afford to fit a cubic design of three levels to estimate a model Quadratic , and biased linear models estimated that the gradient was zero. Box’s design lowered experimentation costs so that a quadratic model could fit, leading to a (long-sought) direction of ascent.
