10 Replicación en R de caso de estudio: Thommes y Kleinebudde (2007)

Properties of pellets manufactured by wet extrusion/spheronization process using κ-carrageenan: Effect of process parameters

11 Artículo de estudio

Librerías requeridas: FrF2, dplyr, knitr, flextable

Los pellets, esferas con un diámetro promedio entre 0.5 y 2 mm y distribución de tamaño estrecha, han despertado gran interés en el desarrollo de formas farmacéuticas de liberación modificada. La técnica de extrusión–esferonización húmeda, utilizada para su preparación, consta de tres etapas principales: extrusión, esferonización y secado en lecho fluido. En el este estudio publicado por (Thommes y Kleinebudde 2007), se evaluaron los parámetros del proceso de peletización (ver Tabla 16.1) en formulaciones que contienen κ-carragenina a través de un diseño \(2^4\) no replicado con tres puntos centrales.

Nota

Véase “Guía para la implementación de diseños experimentales en la industria farmacéutica” para una explicación detallada de los cálculos presentados.

Variables	Nivel (-1)	Nivel (0)	Nivel (1)
Velocidad del tornillo (SCREWSPE)	50 rpm	125 rpm	200 rpm
Número de orificios de la matriz de extrusión (HOLES)	3	13	23
Velocidad de rotación del esferonizador (SPHESPE)	500 rpm	750 rpm	1000 rpm
Temperatura del esferonizador (SPHETEMP )	15°C	30°C	45°C

Tabla 11.1: Factores y niveles considerados por Thommes y Kleinebudde (2007)

Las matrices del diseño en unidades codificadas y en unidades naturales se presentan en la Tabla 16.2. Las variables respuesta evaluadas fueron:

Aspect Ratio (ASPRAT): Relación de diámetros que caracteriza la esfericidad de los pellets.
Equivalent Diameter (DIM): Diámetro calculado a partir del área proyectada del pellet.
10% Interval (INT10): Proporción de partículas cuyo diámetro se encuentra en el rango de 0.9 a 1.1 veces el diámetro promedio.
Coarse Fraction (COARFRA): Proporción de partículas con diámetro relativo mayor a 1.2 veces el diámetro promedio.
Fine Fraction (FINFRA): Proporción de partículas con diámetro relativo menor a 0.8 veces el diámetro promedio.
Tensile Strength (TENSILE): Resistencia mecánica de los pellets.
Mean Dissolution Time (MDT): Tiempo medio de disolución.

12 Construcción del diseño factorial completo 2⁴ no replicado con puntos centrales

A continuación se presenta la réplica del artículo presentado por Thommes y Kleinebudde (2007)

Código

# Variables respuesta

ASPRAT <- c(1.24, 1.13, 1.56, 1.52, 1.07, 1.06, 
            1.07, 1.08, 1.24, 1.09, 1.54, 1.52, 
            1.07, 1.08, 1.06, 1.07, 1.13, 1.08, 1.08)
DIAM <- c(1.54, 1.51, 1.47, 1.47, 1.39, 1.32, 
          1.22, 1.26, 1.55, 1.48, 1.49, 1.50, 
          1.25, 1.24, 1.26, 1.27, 1.36, 1.34, 1.34)
INT10 <- c(65.6, 67.8, 52.2, 49.8, 
           57.0,63.6, 55.6, 63.8, 
           63.0, 65.2, 50.0, 46.2, 
           40.2, 28.8, 54.8, 65.2, 
           68.2, 62.0, 65.6)
COARFRA <- c(0.6, 1.2, 9.0, 7.6, 0.4, 1.4, 
             4.6, 1.4, 1.8, 1.4, 10.8, 8.8, 
             10.0, 9.6, 1.6, 1.2, 0.2, 1.2, 1.8)
FINFRA <- c(5.0, 2.6, 6.4, 9.0, 14.8, 
            8.2, 8.4, 7.0, 5.4, 6.8, 
            6.0, 9.8, 19.6, 31.8, 13.2, 
            5.4, 4.2, 8.6, 6.0)
TENSILE <- c(0.59, 0.58, 0.74, 0.85, 0.63, 
             0.62, 0.48, 0.65, 0.57, 0.54, 
             0.95, 0.94, 0.56, 0.64, 0.64, 
             0.66, 0.54, 0.58, 0.55)
MDT <- c(7.98, 7.90, 6.62, 6.12, 7.66, 
         7.03, 6.35, 7.60, 7.45, 8.05, 
         6.76, 6.48, 6.94, 6.99, 6.75, 
         6.78, 7.31, 7.35, 7.51)

# Diseño de variables codificadas

dis1_cod <- data.frame(
  SCREWSPE = c(rep(c(-1,1),8), rep(0,3)),
  HOLES = c(rep(c(rep(-1,2), rep(1,2)), 4), rep(0,3)),
  SPHESPE = c(rep(c(rep(-1,4), rep(1,4)), 2), rep(0,3)),
  SPHETEMP = c(rep(c(rep(-1,8), rep(1,8)), 1), rep(0,3)))

# Diseño de variables naturales

dis1_nat <- data.frame(
  SCREWSPE = c(rep(c(50,200),8), rep(125,3)),
  HOLES = c(rep(c(rep(3,2), rep(23,2)), 4), rep(13,3)),
  SPHESPE = c(rep(c(rep(500,4), rep(1000,4)), 2), rep(750,3)),
  SPHETEMP = c(rep(c(rep(15,8), rep(45,8)), 1), rep(30,3)))

SCREWSPE(c)	HOLES(c)	SPHESPE(c)	SPHETEMP(c)	SCREWSPE	HOLES	SPHESPE	SPHETEMP	ASPRAT	DIAM	INT10	COARFRA	FINFRA	TENSILE	MDT
-1	-1	-1	-1	50	3	500	15	1.24	1.54	65.6	0.6	5.0	0.59	7.98
1	-1	-1	-1	200	3	500	15	1.13	1.51	67.8	1.2	2.6	0.58	7.90
-1	1	-1	-1	50	23	500	15	1.56	1.47	52.2	9.0	6.4	0.74	6.62
1	1	-1	-1	200	23	500	15	1.52	1.47	49.8	7.6	9.0	0.85	6.12
-1	-1	1	-1	50	3	1,000	15	1.07	1.39	57.0	0.4	14.8	0.63	7.66
1	-1	1	-1	200	3	1,000	15	1.06	1.32	63.6	1.4	8.2	0.62	7.03
-1	1	1	-1	50	23	1,000	15	1.07	1.22	55.6	4.6	8.4	0.48	6.35
1	1	1	-1	200	23	1,000	15	1.08	1.26	63.8	1.4	7.0	0.65	7.60
-1	-1	-1	1	50	3	500	45	1.24	1.55	63.0	1.8	5.4	0.57	7.45
1	-1	-1	1	200	3	500	45	1.09	1.48	65.2	1.4	6.8	0.54	8.05
-1	1	-1	1	50	23	500	45	1.54	1.49	50.0	10.8	6.0	0.95	6.76
1	1	-1	1	200	23	500	45	1.52	1.50	46.2	8.8	9.8	0.94	6.48
-1	-1	1	1	50	3	1,000	45	1.07	1.25	40.2	10.0	19.6	0.56	6.94
1	-1	1	1	200	3	1,000	45	1.08	1.24	28.8	9.6	31.8	0.64	6.99
-1	1	1	1	50	23	1,000	45	1.06	1.26	54.8	1.6	13.2	0.64	6.75
1	1	1	1	200	23	1,000	45	1.07	1.27	65.2	1.2	5.4	0.66	6.78
0	0	0	0	125	13	750	30	1.13	1.36	68.2	0.2	4.2	0.54	7.31
0	0	0	0	125	13	750	30	1.08	1.34	62.0	1.2	8.6	0.58	7.35
0	0	0	0	125	13	750	30	1.08	1.34	65.6	1.8	6.0	0.55	7.51
(c): notación codificadas (n) notación natural

Tabla 12.1: Diseño factorial 2^4 no replicado con puntos centrales

12.1 `ASPRAT`

Código

mod1_cod <- lm(ASPRAT~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod1_cod)


Call:
lm.default(formula = ASPRAT ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.114211  0.002039  0.013289  0.027039  0.043289 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        1.194e+00  1.427e-02  83.716 1.45e-15 ***
SCREWSPE          -1.875e-02  1.554e-02  -1.206 0.255509    
HOLES              9.000e-02  1.554e-02   5.790 0.000175 ***
SPHESPE           -1.425e-01  1.554e-02  -9.167 3.51e-06 ***
SPHETEMP          -3.750e-03  1.554e-02  -0.241 0.814246    
SCREWSPE:HOLES     1.375e-02  1.554e-02   0.885 0.397178    
SCREWSPE:SPHESPE   2.125e-02  1.554e-02   1.367 0.201565    
SCREWSPE:SPHETEMP  4.332e-17  1.554e-02   0.000 1.000000    
HOLES:SPHESPE     -9.000e-02  1.554e-02  -5.790 0.000175 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.06218 on 10 degrees of freedom
Multiple R-squared:  0.9395,    Adjusted R-squared:  0.8911 
F-statistic:  19.4 on 8 and 10 DF,  p-value: 3.893e-05

12.2 `DIM`

Código

mod2_cod <- lm(DIAM~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod2_cod)


Call:
lm.default(formula = DIAM ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.053355 -0.022730 -0.005855  0.024145  0.069145 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        1.382e+00  9.878e-03 139.912  < 2e-16 ***
SCREWSPE          -7.500e-03  1.076e-02  -0.697   0.5019    
HOLES             -2.125e-02  1.076e-02  -1.974   0.0766 .  
SPHESPE           -1.125e-01  1.076e-02 -10.451 1.06e-06 ***
SPHETEMP          -8.750e-03  1.076e-02  -0.813   0.4352    
SCREWSPE:HOLES     1.500e-02  1.076e-02   1.393   0.1937    
SCREWSPE:SPHESPE   3.750e-03  1.076e-02   0.348   0.7348    
SCREWSPE:SPHETEMP -5.721e-17  1.076e-02   0.000   1.0000    
HOLES:SPHESPE     -2.500e-03  1.076e-02  -0.232   0.8210    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.04306 on 10 degrees of freedom
Multiple R-squared:  0.9209,    Adjusted R-squared:  0.8576 
F-statistic: 14.55 on 8 and 10 DF,  p-value: 0.0001416

12.3 `INT10`

Código

mod3_cod <- lm(INT10~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod3_cod)


Call:
lm.default(formula = INT10 ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
    Min      1Q  Median      3Q     Max 
-16.109  -5.034  -1.109   5.553  11.116 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         57.084      2.096  27.230 1.03e-10 ***
SCREWSPE             0.750      2.284   0.328   0.7495    
HOLES               -0.850      2.284  -0.372   0.7176    
SPHESPE             -1.925      2.284  -0.843   0.4191    
SPHETEMP            -3.875      2.284  -1.696   0.1207    
SCREWSPE:HOLES       0.800      2.284   0.350   0.7335    
SCREWSPE:SPHESPE     0.975      2.284   0.427   0.6786    
SCREWSPE:SPHETEMP   -1.075      2.284  -0.471   0.6480    
HOLES:SPHESPE        7.075      2.284   3.097   0.0113 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9.138 on 10 degrees of freedom
Multiple R-squared:  0.5825,    Adjusted R-squared:  0.2485 
F-statistic: 1.744 on 8 and 10 DF,  p-value: 0.202

12.4 `COARFRA`

Código

mod4_cod <- lm(COARFRA~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod4_cod)


Call:
lm.default(formula = COARFRA ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.7263 -2.1263 -0.0013  1.3737  4.0987 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         3.9263     0.7078   5.547 0.000245 ***
SCREWSPE           -0.3875     0.7713  -0.502 0.626287    
HOLES               1.1625     0.7713   1.507 0.162707    
SPHESPE            -0.6875     0.7713  -0.891 0.393711    
SPHETEMP            1.1875     0.7713   1.540 0.154701    
SCREWSPE:HOLES     -0.4875     0.7713  -0.632 0.541560    
SCREWSPE:SPHESPE    0.0125     0.7713   0.016 0.987389    
SCREWSPE:SPHETEMP  -0.0125     0.7713  -0.016 0.987389    
HOLES:SPHESPE      -2.7375     0.7713  -3.549 0.005277 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.085 on 10 degrees of freedom
Multiple R-squared:  0.6514,    Adjusted R-squared:  0.3725 
F-statistic: 2.335 on 8 and 10 DF,  p-value: 0.1045

12.5 `FINFRA`

Código

mod5_cod <- lm(FINFRA~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod5_cod)


Call:
lm.default(formula = FINFRA ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.4539 -2.1414  0.3961  1.9711 10.3961 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         9.3789     1.2238   7.664 1.71e-05 ***
SCREWSPE            0.1125     1.3336   0.084   0.9344    
HOLES              -1.8125     1.3336  -1.359   0.2040    
SPHESPE             3.5875     1.3336   2.690   0.0227 *  
SPHETEMP            2.2875     1.3336   1.715   0.1171    
SCREWSPE:HOLES     -0.4625     1.3336  -0.347   0.7359    
SCREWSPE:SPHESPE   -0.5625     1.3336  -0.422   0.6821    
SCREWSPE:SPHETEMP   1.0875     1.3336   0.815   0.4338    
HOLES:SPHESPE      -3.2375     1.3336  -2.428   0.0356 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.334 on 10 degrees of freedom
Multiple R-squared:  0.6539,    Adjusted R-squared:  0.3769 
F-statistic: 2.361 on 8 and 10 DF,  p-value: 0.1017

12.6 `TENSILE`

Código

mod6_cod <- lm(TENSILE~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod6_cod)


Call:
lm.default(formula = TENSILE ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.10790 -0.04040  0.01086  0.04961  0.08586 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.64789    0.01814  35.711 7.04e-12 ***
SCREWSPE           0.02000    0.01977   1.012  0.33558    
HOLES              0.07375    0.01977   3.730  0.00391 ** 
SPHESPE           -0.05500    0.01977  -2.782  0.01939 *  
SPHETEMP           0.02250    0.01977   1.138  0.28163    
SCREWSPE:HOLES     0.01625    0.01977   0.822  0.43028    
SCREWSPE:SPHESPE   0.01250    0.01977   0.632  0.54141    
SCREWSPE:SPHETEMP -0.01250    0.01977  -0.632  0.54141    
HOLES:SPHESPE     -0.07625    0.01977  -3.857  0.00318 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.07908 on 10 degrees of freedom
Multiple R-squared:  0.8013,    Adjusted R-squared:  0.6423 
F-statistic:  5.04 on 8 and 10 DF,  p-value: 0.01012

12.7 `MDT`

Código

mod7_cod <- lm(MDT~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis1_cod)
summary(mod7_cod)


Call:
lm.default(formula = MDT ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis1_cod)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.53342 -0.21842 -0.00842  0.24033  0.51658 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        7.13842    0.09448  75.552 4.03e-15 ***
SCREWSPE           0.02750    0.10296   0.267  0.79483    
HOLES             -0.40875    0.10296  -3.970  0.00264 ** 
SPHESPE           -0.07875    0.10296  -0.765  0.46203    
SPHETEMP          -0.06625    0.10296  -0.643  0.53441    
SCREWSPE:HOLES     0.03500    0.10296   0.340  0.74094    
SCREWSPE:SPHESPE   0.06000    0.10296   0.583  0.57297    
SCREWSPE:SPHETEMP  0.02250    0.10296   0.219  0.83141    
HOLES:SPHESPE      0.26625    0.10296   2.586  0.02714 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4118 on 10 degrees of freedom
Multiple R-squared:  0.7061,    Adjusted R-squared:  0.4709 
F-statistic: 3.003 on 8 and 10 DF,  p-value: 0.05338

13 Diseño factorial \(2^4\) no replicado sin puntos centrales

Código

# Diseño de variables codificadas

ASPRATspc <- ASPRAT[-c(17:19)]
DIAMspc <- DIAM[-c(17:19)]
INT10spc <- INT10[-c(17:19)]
COARFRAspc <- COARFRA[-c(17:19)]
FINFRAspc <- FINFRA[-c(17:19)]
TENSILEspc <- TENSILE[-c(17:19)]
MDTspc <- MDT[-c(17:19)]

dis2_cod <- data.frame(
  SCREWSPE = c(rep(c(-1,1),8)),
  HOLES = c(rep(c(rep(-1,2), rep(1,2)), 4)),
  SPHESPE = c(rep(c(rep(-1,4), rep(1,4)), 2)),
  SPHETEMP = c(rep(c(rep(-1,8), rep(1,8)), 1)),
  ASPRATspc, DIAMspc, INT10spc, COARFRAspc, FINFRAspc, TENSILEspc, MDTspc)

# Diseño de variables naturales

dis2_nat <- data.frame(
  SCREWSPE = c(rep(c(50,200),8)),
  HOLES = c(rep(c(rep(3,2), rep(23,2)), 4)),
  SPHESPE = c(rep(c(rep(500,4), rep(1000,4)), 2)),
  SPHETEMP = c(rep(c(rep(15,8), rep(45,8)), 1)),
  ASPRATspc, DIAMspc, INT10spc, COARFRAspc, FINFRAspc, TENSILEspc, MDTspc)

13.1 `ASPRAT`

Código

mod12_cod <- lm(ASPRATspc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod12_cod)


Call:
lm.default(formula = ASPRATspc ~ SCREWSPE + HOLES + SPHESPE + 
    SPHETEMP + SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + 
    HOLES:SCREWSPE + HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.02750 -0.01063  0.00125  0.01063  0.02500 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        1.213e+00  5.261e-03 230.468 7.64e-15 ***
SCREWSPE          -1.875e-02  5.261e-03  -3.564  0.00917 ** 
HOLES              9.000e-02  5.261e-03  17.107 5.72e-07 ***
SPHESPE           -1.425e-01  5.261e-03 -27.086 2.40e-08 ***
SPHETEMP          -3.750e-03  5.261e-03  -0.713  0.49904    
SCREWSPE:HOLES     1.375e-02  5.261e-03   2.614  0.03473 *  
SCREWSPE:SPHESPE   2.125e-02  5.261e-03   4.039  0.00494 ** 
SCREWSPE:SPHETEMP  4.625e-17  5.261e-03   0.000  1.00000    
HOLES:SPHESPE     -9.000e-02  5.261e-03 -17.107 5.72e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.02104 on 7 degrees of freedom
Multiple R-squared:  0.9949,    Adjusted R-squared:  0.989 
F-statistic: 169.4 on 8 and 7 DF,  p-value: 2.576e-07

13.2 `DIM`

Código

mod22_cod <- lm(DIAMspc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod22_cod)


Call:
lm.default(formula = DIAMspc ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.06000 -0.01937  0.00125  0.02063  0.06250 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        1.389e+00  1.110e-02 125.110 5.50e-13 ***
SCREWSPE          -7.500e-03  1.110e-02  -0.676   0.5209    
HOLES             -2.125e-02  1.110e-02  -1.914   0.0971 .  
SPHESPE           -1.125e-01  1.110e-02 -10.135 1.96e-05 ***
SPHETEMP          -8.750e-03  1.110e-02  -0.788   0.4564    
SCREWSPE:HOLES     1.500e-02  1.110e-02   1.351   0.2186    
SCREWSPE:SPHESPE   3.750e-03  1.110e-02   0.338   0.7454    
SCREWSPE:SPHETEMP -1.464e-17  1.110e-02   0.000   1.0000    
HOLES:SPHESPE     -2.500e-03  1.110e-02  -0.225   0.8282    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.0444 on 7 degrees of freedom
Multiple R-squared:  0.9399,    Adjusted R-squared:  0.8712 
F-statistic: 13.68 on 8 and 7 DF,  p-value: 0.001237

13.3 `INT10`

Código

mod32_cod <- lm(INT10spc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod32_cod)


Call:
lm.default(formula = INT10spc ~ SCREWSPE + HOLES + SPHESPE + 
    SPHETEMP + SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + 
    HOLES:SCREWSPE + HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
    Min      1Q  Median      3Q     Max 
-14.575  -3.550  -0.175   4.312  10.325 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         55.550      2.270  24.472 4.85e-08 ***
SCREWSPE             0.750      2.270   0.330   0.7508    
HOLES               -0.850      2.270  -0.374   0.7192    
SPHESPE             -1.925      2.270  -0.848   0.4245    
SPHETEMP            -3.875      2.270  -1.707   0.1316    
SCREWSPE:HOLES       0.800      2.270   0.352   0.7349    
SCREWSPE:SPHESPE     0.975      2.270   0.430   0.6805    
SCREWSPE:SPHETEMP   -1.075      2.270  -0.474   0.6502    
HOLES:SPHESPE        7.075      2.270   3.117   0.0169 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9.08 on 7 degrees of freedom
Multiple R-squared:  0.6687,    Adjusted R-squared:  0.2901 
F-statistic: 1.766 on 8 and 7 DF,  p-value: 0.2339

13.4 `COARFRA`

Código

mod42_cod <- lm(COARFRAspc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod42_cod)


Call:
lm.default(formula = COARFRAspc ~ SCREWSPE + HOLES + SPHESPE + 
    SPHETEMP + SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + 
    HOLES:SCREWSPE + HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.6375 -1.1625 -0.0375  1.0875  3.5625 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         4.4625     0.7604   5.869 0.000619 ***
SCREWSPE           -0.3875     0.7604  -0.510 0.625996    
HOLES               1.1625     0.7604   1.529 0.170155    
SPHESPE            -0.6875     0.7604  -0.904 0.395969    
SPHETEMP            1.1875     0.7604   1.562 0.162329    
SCREWSPE:HOLES     -0.4875     0.7604  -0.641 0.541859    
SCREWSPE:SPHESPE    0.0125     0.7604   0.016 0.987343    
SCREWSPE:SPHETEMP  -0.0125     0.7604  -0.016 0.987343    
HOLES:SPHESPE      -2.7375     0.7604  -3.600 0.008738 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.042 on 7 degrees of freedom
Multiple R-squared:  0.7331,    Adjusted R-squared:  0.428 
F-statistic: 2.403 on 8 and 7 DF,  p-value: 0.1325

13.5 `FINFRA`

Código

mod52_cod <- lm(FINFRAspc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod52_cod)


Call:
lm.default(formula = FINFRAspc ~ SCREWSPE + HOLES + SPHESPE + 
    SPHETEMP + SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + 
    HOLES:SCREWSPE + HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
   Min     1Q Median     3Q    Max 
-7.037 -2.606 -0.050  2.438  9.812 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         9.9625     1.4646   6.802 0.000253 ***
SCREWSPE            0.1125     1.4646   0.077 0.940923    
HOLES              -1.8125     1.4646  -1.238 0.255795    
SPHESPE             3.5875     1.4646   2.449 0.044145 *  
SPHETEMP            2.2875     1.4646   1.562 0.162300    
SCREWSPE:HOLES     -0.4625     1.4646  -0.316 0.761378    
SCREWSPE:SPHESPE   -0.5625     1.4646  -0.384 0.712338    
SCREWSPE:SPHETEMP   1.0875     1.4646   0.743 0.481948    
HOLES:SPHESPE      -3.2375     1.4646  -2.210 0.062756 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.859 on 7 degrees of freedom
Multiple R-squared:  0.6911,    Adjusted R-squared:  0.3381 
F-statistic: 1.958 on 8 and 7 DF,  p-value: 0.1957

13.6 `TENSILE`

Código

mod62_cod <- lm(TENSILEspc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod62_cod)


Call:
lm.default(formula = TENSILEspc ~ SCREWSPE + HOLES + SPHESPE + 
    SPHETEMP + SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + 
    HOLES:SCREWSPE + HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.07125 -0.03625  0.00125  0.03875  0.06875 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.66500    0.01691  39.327 1.79e-09 ***
SCREWSPE           0.02000    0.01691   1.183  0.27552    
HOLES              0.07375    0.01691   4.361  0.00331 ** 
SPHESPE           -0.05500    0.01691  -3.253  0.01401 *  
SPHETEMP           0.02250    0.01691   1.331  0.22503    
SCREWSPE:HOLES     0.01625    0.01691   0.961  0.36857    
SCREWSPE:SPHESPE   0.01250    0.01691   0.739  0.48382    
SCREWSPE:SPHETEMP -0.01250    0.01691  -0.739  0.48382    
HOLES:SPHESPE     -0.07625    0.01691  -4.509  0.00277 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.06764 on 7 degrees of freedom
Multiple R-squared:  0.8873,    Adjusted R-squared:  0.7585 
F-statistic:  6.89 on 8 and 7 DF,  p-value: 0.009795

13.7 `MDT`

Código

mod72_cod <- lm(MDTspc~SCREWSPE+HOLES+SPHESPE+SPHETEMP+
                 SCREWSPE:HOLES+SCREWSPE:SPHESPE+SCREWSPE:SPHETEMP+
                 HOLES:SCREWSPE+HOLES:SPHESPE+
                 SCREWSPE:SPHETEMP, data=dis2_cod)
summary(mod72_cod)


Call:
lm.default(formula = MDTspc ~ SCREWSPE + HOLES + SPHESPE + SPHETEMP + 
    SCREWSPE:HOLES + SCREWSPE:SPHESPE + SCREWSPE:SPHETEMP + HOLES:SCREWSPE + 
    HOLES:SPHESPE + SCREWSPE:SPHETEMP, data = dis2_cod)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.4863 -0.1856  0.0025  0.1475  0.5637 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)        7.09125    0.11371  62.360 7.16e-11 ***
SCREWSPE           0.02750    0.11371   0.242   0.8158    
HOLES             -0.40875    0.11371  -3.595   0.0088 ** 
SPHESPE           -0.07875    0.11371  -0.693   0.5109    
SPHETEMP          -0.06625    0.11371  -0.583   0.5784    
SCREWSPE:HOLES     0.03500    0.11371   0.308   0.7672    
SCREWSPE:SPHESPE   0.06000    0.11371   0.528   0.6141    
SCREWSPE:SPHETEMP  0.02250    0.11371   0.198   0.8488    
HOLES:SPHESPE      0.26625    0.11371   2.341   0.0517 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4549 on 7 degrees of freedom
Multiple R-squared:  0.7378,    Adjusted R-squared:  0.438 
F-statistic: 2.462 on 8 and 7 DF,  p-value: 0.1262

14 Comparación de los coeficientes encontrados en el diseño factorial completo \(2^4\) con y sin puntos centrales

ASPRAT	ASPRATspc	DIAM	DIAMspc	INT10	INT10spc	COARFRA	COARFRAspc	FINFRA	FINFRAspc	TENSILE	TENSILEspc	MDT	MDTspc
1.19421	1.21250	1.38211	1.38875	57.08421	55.550	3.92632	4.4625	9.37895	9.9625	0.64789	0.66500	7.13842	7.09125
-0.01875	-0.01875	-0.00750	-0.00750	0.75000	0.750	-0.38750	-0.3875	0.11250	0.1125	0.02000	0.02000	0.02750	0.02750
0.09000	0.09000	-0.02125	-0.02125	-0.85000	-0.850	1.16250	1.1625	-1.81250	-1.8125	0.07375	0.07375	-0.40875	-0.40875
-0.14250	-0.14250	-0.11250	-0.11250	-1.92500	-1.925	-0.68750	-0.6875	3.58750	3.5875	-0.05500	-0.05500	-0.07875	-0.07875
-0.00375	-0.00375	-0.00875	-0.00875	-3.87500	-3.875	1.18750	1.1875	2.28750	2.2875	0.02250	0.02250	-0.06625	-0.06625
0.01375	0.01375	0.01500	0.01500	0.80000	0.800	-0.48750	-0.4875	-0.46250	-0.4625	0.01625	0.01625	0.03500	0.03500
0.02125	0.02125	0.00375	0.00375	0.97500	0.975	0.01250	0.0125	-0.56250	-0.5625	0.01250	0.01250	0.06000	0.06000
0.00000	0.00000	0.00000	0.00000	-1.07500	-1.075	-0.01250	-0.0125	1.08750	1.0875	-0.01250	-0.01250	0.02250	0.02250
-0.09000	-0.09000	-0.00250	-0.00250	7.07500	7.075	-2.73750	-2.7375	-3.23750	-3.2375	-0.07625	-0.07625	0.26625	0.26625
spc: sin puntos centrales

Tabla 14.1: Comparación de los coeficientes encontrados en el diseño factorial completo \(2^4\) con y sin puntos centrales

Thommes, Markus, y Peter Kleinebudde. 2007. «Properties of pellets manufactured by wet extrusion/spheronization process using \(\kappa\)-carrageenan: Effect of process parameters». AAPS PharmSciTech 8 (4): 95.

Volver arriba

11 Artículo de estudio

12 Construcción del diseño factorial completo 2⁴ no replicado con puntos centrales

12.1 ASPRAT

12.2 DIM

12.3 INT10

12.4 COARFRA

12.5 FINFRA

12.6 TENSILE

12.7 MDT

13 Diseño factorial \(2^4\) no replicado sin puntos centrales

13.1 ASPRAT

13.2 DIM

13.3 INT10

13.4 COARFRA

13.5 FINFRA

13.6 TENSILE

13.7 MDT

14 Comparación de los coeficientes encontrados en el diseño factorial completo \(2^4\) con y sin puntos centrales

12.1 `ASPRAT`

12.2 `DIM`

12.3 `INT10`

12.4 `COARFRA`

12.5 `FINFRA`

12.6 `TENSILE`

12.7 `MDT`

13.1 `ASPRAT`

13.2 `DIM`

13.3 `INT10`

13.4 `COARFRA`

13.5 `FINFRA`

13.6 `TENSILE`

13.7 `MDT`