Applications of Response Surface Methodology (RSM) in Product Design, Development, and Process Optimization

1. Introduction

Experimentation, Data collection, Data processing, and Analysis of data are very basic and essential to Scientists, Engineers, Technologists, and Manufacturing Industries to design, develop, improve and validate their products, processes, and operations. Response surface methodology (RSM) which is available in MINITAB and other proprietary software is a collection of both statistical and mathematical techniques useful for developing, improving, and optimizing processes [1]. RSM is known to play a pivotal role in new product design and development as well as in improving existing ones. With response surface methodology we can determine the optimum factor needed to produce the best result. RSM is a critical and very robust tool for data manipulation and analysis of research data to obtain a quality result or an improvement [1]. RSM could be applied by an industry that desires to manufacture a component (from Al-Si Alloy material) with minimum surface roughness by combining three controllable variables (cutting speed, feed rate, and, depth of cut). Because of this, the Design of Experiments (DOE) could be used to carry out the study of the effect of the three machining variables (cutting speed, feed rate, and depth of cut) on the surface roughness (Ra) of Al-Si alloy [2]. With the use of response surface methodology (RSM), a mathematical prediction model of the surface roughness would be developed in terms of cutting speed, feed rate, and depth of cut. The effects of the three process parameters on both Ra can then be investigated by using the response surface methodology (RSM). The above approach can be adopted by any industry, scientist, or researcher in getting better results (response) from several variables otherwise known as factors. RSM helps to reduce the noise in an experiment, thereby ensuring optimization. Many researchers have conducted researches on the application of RSM or other DOE concept in which the results of their findings have been used to develop a predictive model in several fields such as; tool life modeling, surface roughness prediction, for monitoring and functionality or health condition of electronic devices also for the surface roughness of Inconel using full factorial design of experiment among other areas of applications [2, 3, 4]. The RSM looks into an adequate approximation relationship between input and output variables and determines the best operating circumstances for a system under study or a portion of the factor field that complies with the operating requirements or conditions [3, 5, 6].

Response surface methodology can be better referred to as a collection of statistical and mathematical techniques employed for product design and improvement, process development and improvement as well as process optimization. It has major applications in the design, development, and, formulation of new products as well as in improving existing product design. RSM is a robust tool for the design of experiments, analysis of experimental data, and process optimization. In RSM, the response is determined by the variables and the aim is to optimize the response [1, 7, 8]. There are two primary experimental designs used in response surface methodology: Box-Behnken designs (BBD) and central composite designs (CCD) [8, 9]. Recently, optimization studies have also used central composite rotatable design (CCRD) and face central composite design (FCCD) [8, 10, 11, 12, 13, 14].

Wong [15] employed RSM concept to carry out reliability analysis of soil slopes. Tandjiria et al. [16] used response surface method for reliability analysis of laterally loaded piles. Sivakumar Babu and Amit Srivastava [17] presented a study on the analysis of allowable bearing pressures on shallow foundation using response surface method and showed that a comparative study of the results of the analysis from conventional solution and numerical analysis in terms of reliability indices enables rational choice of allowable loads. For better understanding of the RSM concept in our daily life experiences as described in Figure 1. Take for example we have two variables (humidity and temperature) and we want to see the effects of these variables on human comfort. We can name these independent variables temperature and humidity, X1 and X2 and the response which is human comfort can be named Y. Response Surface Methodology is useful in this case for the modeling and optimization of the situation above in which the response of interest (human comfort) is influenced by the variables (humidity and temperature). In this model example, our objective is to optimize this response The visual representation of the above is otherwise known as Response Surface Methodology (RSM) or response surface modeling. To find the levels of temperature (X1) and pressure (X2) for maximum human comfort (y) in the above process.

y=x1x2+ϵ

E1

ϵ is referred to as the error term inherent in the system

1.1 The concept of RSM

The concept of Response Surface Methodology can be used to establish an approximate explicit functional relationship between input random variables and output response through regression analysis and probabilistic analysis can be performed [15]. RSM involves a combination of metamodeling (i.e., regression) and sequential procedures (iterative optimization). Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems. By careful design of experiments, the objective is to optimize a response (output variable) that is influenced by several independent variables (input variables). A collection of mathematical and statistical methods called Response Surface Methodology (RSM) can be used to simulate and analyze issues. The goal of meticulous experiment design is to maximize a response (output variable) that is affected by a number of independent variables (input variables). The motivation behind this work is the applicability of the concept of RSM to many areas of scientific research, engineering and manufacturing industries.

1.2 Objective of this present study

The applications of RSM is for product and process development are discussed through some general and scenario applications. The chapter review presented, is shown that with RSM we can;

1. identify the sensitive parameter that provides the greatest influence on the response.

2. easily take decision that will impact positively the product design and process optimization.

3. ensure reliability, acceptability and profitability of the product developed and/or optimized condition.