Table 1. The central composite design (CCD) with three central points employed for two independent variables

Sample no.	Variables		Coded levels		CSF^a
Sample no.	Time (min) X₁	Acid concentration (mM) X₂	Time χ₁	Acid concentration χ₂	CSF^a
1	30	82(pH :1.35)	0	0	1.89
2	30	82(pH :1.35)	0	0	1.89
3	30	82(pH :1.35)	0	0	1.89
4	50	122(pH :1.18)	1	1	2.29
5	10	122(pH :1.18)	−1	1	1.59
6	50	41(pH :1.55)	1	−1	1.92
7	10	41(pH :1.55)	−1	−1	1.22
8	30	139(pH :1.16)	0	1.4	2.08
9	58	82(pH :1.35)	1.4	0	2.18
10	30	24(pH :1.72)	0	−1.4	1.52
11	2	82(pH :1.35)	−1.4	0	0.72

Reaction temperature fixed to 160°C.
Combined severity factor (CSF) = log{t × exp[(TH−TR)/14.75]}−pH (t is the reaction time for the pretreatment in minutes, TH is the reaction temperature in °C, and TR is the reference temperature, most often 100°C(8).