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What is Standard Deviation Method

Chapter 17
Handbook of Research on Artificial Intelligence Techniques and Algorithms
A method associated with statistics and probability theory which is used to find the variation or dispersion of each variance from the average exists. It is most widely used to measure dispersion of a series and is commonly denoted by the symbol ‘s’. The standard deviation method is defined as the square-root of the average of squares of deviations, when such deviations for the values of individual items in a series are obtained from the arithmetic average. The mathematical representation of this method is as follows: or in case of frequency distribution where, X i = i th value of the variable X; = Arithmetic average; n= Number of items; f i = The frequency of the i th item.
Published in Chapter:
Application of Standard Deviation Method Integrated PSO Approach in Optimization of Manufacturing Process Parameters
Arindam Majumder (National Institute of Technology Agartala, India) and Abhishek Majumder (Tripura University, India)
Copyright: © 2015 |Pages: 28
DOI: 10.4018/978-1-4666-7258-1.ch017
Abstract
Multi-objective optimization is one of the most popular research areas in the world of manufacturing. It concerns the manufacturing optimization problems involving more than one optimization simultaneously, but in this present scenario, it is becoming very tough to solve a manufacturing-related multi-objective problem as no logical method has been developed in assignment of response individual weight. Therefore, to tackle this problem, this chapter proposes a new integrated approach by combining Standard Deviation Method with Particle Swarm Optimization. Two examples of optimizing the advanced manufacturing process parameters are performed to test the proposed approach. The examples considered for this approach are also attempted using other established optimization techniques such as Desirability-based RSM and SDM-GA. The results verify the effectiveness of the proposed approach during multi-objective manufacturing process parameter optimization.
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