Abstract
In the case of lack of theoretical knowledge of the relationships between input and outputs variables of a system, we have a second possibility: the experimental reconstruction of these relationships. In the case of theoretical knowledge, the system is represented by linear or nonlinear equations between input and output variables, while in the absence of them an experiment must be planned to reach a certain level of knowledge of the system: the Design of experiment (DOE). This tool is general enough to be applied to different types of variables (e.g. categorical variables). Given the introductory character of this chapter, the presentation is limited to basic aspects.
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Notes
- 1.
E(MSW) is the expected value MSW for an infinite number of repetitions. Assuming the variance \(\sigma ^2\) for each value \(y_{ij}\) as constant, we can assume that: \(E(MSB_c) =\sigma ^2 + V_{col}\). (\(V_{col}\) being the measure of differences among column means.)
- 2.
This may be confusing with respect to the 2-level designs since 0 seems reserved for central points between \(-1 \) and \(+1\). Therefore, in three levels matrices we will use 1, 2, 3 notation that does not necessarily mean that 2 is the midpoint between 1 and 3.
- 3.
The symbols may be letters, numbers, colours, etc. R. A. Fisher promoted the use of Latin squares in experiments in his 1935 book The Design of Experiments. A stained glass window in Gonville and Caius College in Cambridge (UK) commemorates the very important results of his research.
- 4.
Shot peening is a cold working processes in which the surface is bombarded with small shots. The resistance benefit is the result of the effect of compression stress distribution and cold working, both due to the shot induced deformation.
- 5.
The maximum intensity of 16Â A was chosen and then its value was decreased to 12Â A and 8Â A. It is necessary to not exceed the Almen 16Â A intensity in order to avoid a subsequent grinding of the surface to remove the peaks of excessive roughness, which would nullify the positive effect of the treatment.
- 6.
This is for taking into account the uncertainty of the residual stress at the surface, due to the presence of the white layer—an amorphous structure generated by the nitriding process— that confuses the answer of the X-ray diffractometer [5].
- 7.
Hypothetically this value is derived from a large number of observations (\(\infty \)).
References
503 S (2018) Design of experiment. https://onlinecourses.science.psu.edu/stat503/node/1
Bailey RA (2013) Latin squares. http://www.maths.qmul.ac.uk/~rab/gcs2hand.pdf, g. C. Steward lecture, Gonville and Caius College, Cambridge
Berger P (1994) Experimental design: is it important? Lecture handout, MIT Boston Summer Professional Program. http://professional.mit.edu/programs/short-programs/design-and-analysis-experiments
Cristofolini L, Croccolo D, Freddi A (2001) Miglioramento della resistenza a fatica di un acciaio niturato e pallinato. una applicazione del progetto dell’esperimento (DOE). Tratt Finit 41(2):81–88
Croccolo D, Scazzieri F, Freddi A (1999) Resistenza a fatica per flessione alternata di provini in acciaio 32CrMoV13 nitrurato e pallinato. In: Atti XXVIII Convegno AIAS, Organization AIAS, vol 1
DeVor RE, Chang TH, Sutherland JW (1992) Statistical quality design and control. MacMillan Publ. Co, N.Y
Dixon W, Massey F (1969) Introduction to statistical analysis. McGraw-Hill, N.Y
Finney DJ (1955) Experimental design and its statistical basis. University of Chicago Press, Cambridge
Fisher R (1974) The design of experiments, 9th edn. Hafner, N.Y
Freddi A (2004) Imparare a progettare, vol 1, 1st edn. Pitagora Editrice Bologna
Freddi A, Veschi D, Bandini M, Giovani G (1997) Design of experiment to investigate residual stresses and fatigue life improvement by a surface treatment. Fatigue Fract Eng Mater Struct 20(8):1147–1157
Freddi A, Olmi G, Cristofolini L (2015) Experimental stress analysis for materials and structures. In: Stress analysis models for developing design methodologies. Series in solid and structural mechanics, vol 1, 1st edn. Springer
Goos P, Jones B (2011) Optimal design of experiments: a case study approach. Wiley, N.Y
Hardwick C (2017) Practical design of experiments-Doe made easy, minitab statistical software edn
Kacker RN, Lagergren ES, Filliben JJ (1991) Taguchis orthogonal arrays are classical designs of experiments. J Res Natl Inst Stand Technol 96:577591
Mason RL, Gunst RF, Hess JL (2003) Statistical design and analysis of experiments: with applications to engineering and science, 2nd edn. Wiley
Montgomery DC (1991) Design and analysis of experiments. Wiley
Montgomery DC (2012) Design and analysis of experiments (Chapter 12). Wiley
Phadke MS (1989) Quality engineering using robust design. PTR Prentice Hall, Enlewood Cliffs, New Jersey
Soliani L (2003) Statistica applicata alla ricerca biologica e ambientale. UNI, NOVA Parma
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Freddi, A., Salmon, M. (2019). Design of Experiment. In: Design Principles and Methodologies. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-95342-7_6
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