Optimal Tolerance Design and Optimization for a Pharmaceutical Quality Characteristic

Table 2

Experimental data for a pharmaceutical manufacturing process.

Control factors (𝑥)			Destructive quality characteristic; hardness (𝑦)					Surrogate variable; terahertz refractive index (𝑡)
𝑥1	𝑥2	𝑥3	𝑦1	𝑦2	𝑦3	𝜇𝑦	𝑠^2𝑦	𝑡1	𝑡2	𝑡3	𝜇𝑡	𝑠^2𝑡	𝜌𝑦𝑡
−1	−1	−1	6.478	7.518	6.281	6.759	0.442	1.477	1.560	1.407	1.481	0.006	0.948
−1	−1	1	2.000	3.004	2.345	2.450	0.260	1.043	1.180	1.000	1.074	0.009	0.840
−1	1	−1	8.839	10.220	9.088	9.382	0.542	1.670	1.787	1.641	1.699	0.006	0.937
−1	1	1	5.699	6.750	5.581	6.010	0.414	1.403	1.460	1.284	1.382	0.008	0.807
1	−1	−1	5.495	6.817	6.280	6.197	0.443	1.351	1.505	1.343	1.400	0.008	0.779
1	−1	1	9.600	10.570	9.103	9.757	0.554	1.753	1.801	1.648	1.734	0.006	0.922
1	1	−1	4.987	5.985	4.807	5.260	0.403	1.327	1.362	1.205	1.298	0.007	0.774
1	1	1	10.756	11.940	10.510	11.070	0.586	1.903	2.000	1.866	1.923	0.005	0.994
−1.68	0	0	7.113	7.848	6.443	7.135	0.494	1.480	1.523	1.380	1.461	0.005	0.968
1.68	0	0	7.473	8.470	7.143	7.695	0.477	1.570	1.626	1.466	1.554	0.007	0.900
0	−1.68	0	8.657	9.609	8.195	8.820	0.520	1.655	1.718	1.567	1.647	0.006	0.957
0	1.68	0	10.647	12.000	10.557	11.070	0.653	1.828	1.936	1.804	1.856	0.005	0.993
0	0	−1.68	2.705	3.804	3.089	3.199	0.312	1.082	1.213	1.050	1.115	0.007	0.858
0	0	1.68	7.779	8.888	7.546	8.071	0.514	1.610	1.657	1.490	1.586	0.007	0.820
0	0	0	8.431	8.511	7.271	8.071	0.482	1.651	1.561	1.475	1.563	0.008	0.828
0	0	0	7.379	7.286	6.173	6.946	0.451	1.475	1.551	1.383	1.470	0.007	0.858
0	0	0	6.993	7.887	6.521	7.134	0.481	1.519	1.549	1.392	1.487	0.007	0.868
0	0	0	8.856	8.856	7.623	8.445	0.507	1.700	1.609	1.527	1.612	0.008	0.849
0	0	0	7.299	8.657	7.694	7.883	0.488	1.537	1.654	1.480	1.557	0.008	0.818
0	0	0	10.443	10.300	9.092	9.945	0.550	1.739	1.788	1.631	1.720	0.006	0.918