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

Open Access

Table 6

Estimates of the TL SF models' parameters for the responses Y_1er, Y_2er, and Y_3er.

Var.	Param.	Y_1er		Y_2er		Y_3er
		s = 0.1	s = 0.2	s = 0.1	s = 0.2	s = 0.1	s = 0.2
Cte.	β₀	2.059	2.704	0.181	0.181	–2.457	–3.583
ln(x1)	β₁	2.914*	4.020*	0.235	0.235	–4.213	–4.785*
ln(x2)	β₂	0.123	0.219	–0.133	–0.133	–0.584	0.313
ln(x3)	β₃	2.614*	3.577*	0.563	0.563	–2.744	–4.437*
ln(x4)	β₄	–2.652*	–3.638*	–0.492	–0.492	3.572	4.867*
ln(x1)^2	β₅	–1.268	–1.515	–0.107	–0.107	0.972	1.739
ln(x1)*ln(x2)	β₆	–0.123	0.048	–0.006	–0.006	0.935	0.292
ln(x1)*ln(x3)	β₇	–4.000*	–5.789*	–0.585	–0.585	5.635	6.752*
ln(x1)*ln(x4)	β₈	2.680*	3.725*	0.546	0.546	–2.953	–4.483*
ln(x2)^2	β₉	0.063	–0.123	0.151	0.151	0.501	–0.449
ln(x2)*Ln(x3)	β₁₀	–0.204	0.045	0.019	0.019	–0.409	0.074
ln(x2)*Ln(x4)	β₁₁	–0.074	–0.232	–0.025	–0.025	–0.019	0.162
ln(x3)^2	β₁₂	–0.823	–1.448	–0.260	–0.260	0.957	1.746
ln(x3)*Ln(x4)	β₁₃	2.622*	4.161*	0.371	0.371	–3.478	–4.679*
ln(x4)^2	β₁₄	–1.675	–2.482*	–0.205	–0.205	2.102	2.343*
$σ^{2} = σ_{v}^{2} + σ_{u}^{2}$		2.85.10^–2	0.76.10^–2	0.60.10^–3	0.32.10^–2	2,54	–0.37.10^–1
γ		10^–8	10^–8	0.14	0.16.10^–7	0.98	10^–8
Log (likelihood)		34.72	36.73	84.32	52.04	–23.50	8.03

t-test critical value (5% level)=2.12.

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