Robust design optimization of dynamic and static manufacturing processes using the stochastic frontier model

Open Access

Table 1

Mapping between the econometric and the RDPP-SF approach.

Econometric model	RDPP-SF method
Set of DMUs	Design plan (DoE)
DMU(i)	Run, i, in the DoE
Panel/cross data	Replicated/non-replicated dataset
vi: random variation	Statistical random variation
ui: technical inefficiency	Non-random variation (measurement of robustness in the process)

Metric for the RDPP-SF*: (H₀ : γ = 0 vs. H₁ : γ > 0) where $γ = \frac{σ_{u}^{2}}{σ_{v}^{2} + σ_{u}^{2}}$ , Rejected H₀ at α = 5% level if the Likelihood Ratio (LR) exceeds $χ_{1, 2 α = 10 %}^{2} .$

Hypothesis test on robustness. If it is proven statistically significant we should reject the hypothesis saying that the process is fully robust, i.e., under statistical control, solely.

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