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

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Table 5

Hypothesis tests for the regressional model (Y_1er, Y_2er, and Y_3er) and significance of non-random variation.

Tests	Y_1er		Y_2er		Y_3er
	s = 0.1	s = 0.2	s = 0.1	s = 0.2	s = 0.1	s = 0.2
*(H₀: CD vs H₁: TL)	(CD)	(CD)	(TL)	(TL)	(CD)	(CD)
LR statistic	13.22	14.50	18.96	41.48	–49.10	7.20
**(H₀: γ = 0 vs H₁: γ > 0)	Significant	Significant	Significant	Significant	Significant	Significant
LR statistic	153.1	184.32	53.63	105.40	83.03	156.44

*At the 5% level, (H₀: CD vs H₁: TL) test has $χ_{c}^{2} = χ_{10}^{2}$ = 18.31 and (H₀: γ = 0 vs H₁: γ > 0) has $χ_{c}^{2} = χ_{1}^{2} (10 %) = 2.71$ .

**TL (TransLog): Quadratic model, and CD (Cobb-Douglas): Linear model.

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