Abstract. The classic design of experiments (DoE) typically uses the least-square method for a model identification and requires associated assumption about the normality of a noise factor. It is very convenience because it leads to a relative simple computations and well-known asymptotic statistics based on the normality assumption. However, if that assumption is not satisfied it may fail and obtained results may differ radically from the verification tests. The rationale for the caution may be the comparison of interval plots (based on the normality hypothesis) and box-plots (based on raw data). The useful approach is the bootstrap-based methodology which replaces the requirement of the normality assumption with weaker requirement of the independent and identical distribution (i.i.d.) of the random term. The industrial applications of this approach are still rare because the industry is very conservative and
The analysis of variance (ANOVA) is a classic tool for an identification of discreet factors impact on the measurable output by a specific decomposition on a total variance according to the scheme proposed by R.A Fisher in the 1920s. There are many explicit and implicit assumptions required as a preliminary of ANOVA computations. The ANOVA computations scheme is well known and implemented in many types of software but all estimations are provided with the assumption of a normal and homoscedasticity distribution of the noise disturbing the output. Computation procedures produce a single number output (e.g. F statistics, p-Value) without any analysis of their own dispersion. This paper analyzes the ANOVA output using the bootstrap approach. It seems to be the most convenient as a data-driven procedure. The source raw data are taken from the image analysis conducted during the investigation of the impact of the ceramic layer thickness on the wax pattern assembly of a turbine blade on the (γ+γ’) eutectic in the IN713C superalloy.
Design of experiment (DoE) is a methodology widely used in an industry and an academia. However the fundamentals of DoE are well known since first articles of R.A. Fisher, the uncertainty estimation is still the investigated issue due to the fact that non-linear outcome functions do not preserve the normal distribution. The analytical solutions are known only for a very limited number of transformation. Authors propose to involve a bootstrap approach to estimate the outcome uncertainty of the response surface model.
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