Table 1.
Some existing NHPP SRMs.
Fig 1.
S-shaped as a part of function.
Fig 2.
Transformation from to
.
Table 2.
Function when some variables are vanished.
Fig 3.
Numerical illustration of .
Table 3.
Limitations of and
.
Table 4.
Variation table of when b > 0.
Table 5.
Variation table of when b < 0.
Table 6.
Limitations of and
.
Fig 4.
Numerical illustration of .
Table 7.
Variation table of when b > 0 and
.
Table 8.
Variation table of when b > 0 and
.
Table 9.
Variation table of when b < 0 and
.
Table 10.
Variation table of when b < 0 and
.
Table 11.
Limitations of and
.
Table 12.
Variation table of when b > 0,
, and k > 1.
Table 13.
Variation table of when b > 0,
, and 0 < k < 1.
Table 14.
Variation table of when b > 0,
, and –1 < k < 0.
Table 15.
Variation table of when b > 0,
, and k<–1.
Fig 5.
Numerical illustration of when b > 0 and
.
Fig 6.
Numerical illustration of when b < 0 and
.
Fig 7.
Numerical illustration of when
.
Table 16.
Variation table of when b > 0,
, and k > 1.
Table 17.
Variation table of when b > 0,
, and 0 < k < 1.
Table 18.
Variation table of when b > 0,
, and k < 0.
Table 19.
Variation table of when b < 0,
, and k > 1.
Table 20.
Variation table of when b < 0,
, and 0 < k < 1.
Table 21.
Variation table of when b < 0,
, and –1 < k < 0.
Table 22.
Variation table of when b < 0,
, and k<–1.
Table 23.
Variation table of when b < 0,
, and k > 1.
Table 24.
Variation table of when b < 0,
, and 0 < k < 1.
Table 25.
Variation table of when b < 0,
, and k < 0.
Table 26.
Variation table of when k > b or k<–b.
Table 27.
Variation table of when b > k > 0.
Table 28.
Variation table of when 0>k>–b.
Fig 8.
Numerical illustration of .
Table 29.
Rational range of four S-shaped functions.
Fig 9.
Numerical illustration of 4 types of S-shaped function.