Application of the Simultaneous Perturbation Stochastic Approximation Algorithm for Process Optimization: Case Study

Background

When you are trying to improve a process, there are two basic ways to obtain the necessary information: one is to observe or monitor using statistical tools, until you obtain useful signals that allow you to improve it; it is said that this is a passive strategy. The other way is to experiment, making strategic and deliberate changes to the process to provoke these useful signals. Design of experiments (DOE) is a set of active techniques, in the sense that they do not expect the process to send useful signals, but rather that it is “manipulated” to provide the information required for its improvement (Pulido, H. G. et al., 2012) .

The design of experiments is the application of the scientific method to generate knowledge about a system or process, by means of properly planned tests. This methodology has been consolidated as a set of statistical and engineering techniques that allows a better understanding of complex cause-effect situations (Montgomery, 2017).

The objective of a factorial design is to study the effect of different factors on one or several responses, when the same interest is had on all factors (Lujan-Moreno et al., 2018). For example, one of the most important objectives of a factorial design is to determine the combination of levels of controllable factors that will improve process performance.

The factors can be qualitative or quantitative. In order to study the influence of each factor on the response variable, it is necessary to choose at least two test levels for each of them. With a full factorial design, all possible combinations between the levels of the factors to be tested are studied.

However, there are many experimental designs to study the different types of industrial processes. And it is necessary to know how to choose among these types of designs the one that is most appropriate for each situation (Lauro, C. H. et al., 2016) . There are five aspects that influence the selection of an experimental design, in the meaning that when these aspects change, they usually lead us to change the design;

• 1.

  The objective of the experiment,

• 2.

  The number of factors to be studied,

• 3.

  The number of levels tested on each factor,

• 4.

  The affects you are interested in investigating,

• 5.

  The cost of the experiment, the time and the desired precision.

According to their objective, experimental designs can be classified as follows (Pulido & Salazar, 2012):

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  Designs to compare two or more treatments

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    Completely random designs (Montgomery, 2017)

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    Random complete block designs, (Cheng, 2016)

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    Latin Squares designs (Anderson, M. J., & Whitcomb, 2016)

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    Greco-Latin square designs (Montgomery, 2017), (MacCalman, et al., 2017)

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  Designs to study the effect of several factors on one or more response variables

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    2n factorial designs, (Kleijnen, 2015)

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    3n factorial designs, (Malik & Pakzad, 2018)

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    2n-p fractional factorial designs (Douaik, 2016)

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  Designs for process optimization, these can be divided into designs for

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    First-order models

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      2n factorial designs, (Kleijnen, 2015)

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      2n-p fractional factorial designs, (Douaik, 2016), (Kleijnen, 2005)

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      Plackett burman design, (Douaik, 2016), (Kleijnen, 2005)

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      Simplex Design (Briones, F. Z. et al., 2016),

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    and designs for second-order models

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      Central composite design, (Malik & Pakzad, 2018), (Salvatori, P. E. et al., 2018), (Douaik, 2016).

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      Box-Behnken design, (Malik & Pakzad, 2018), (Douaik, 2016)

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      3n factorial designs, (Malik & Pakzad, 2018)

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      3n-p fractional factorial designs (Montgomery, 2017)

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  Robust designs

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    Orthogonal Array Designs(Cheng, 2016), (Dersjö, T., & Olsson, 2012)

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    Design with internal and external arrangement (Heise, S. et al., 2018), (Briones, F. Z. et al., 2016)

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  Mixture design

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    Axial design (Salvatori, P. E. et al.,2018)