Template:Excel (Text, Inputs, Herbst-Fuerstenau, Selection and Breakage)

$Selection={\begin{cases}{\begin{bmatrix}{\begin{bmatrix}S_{1}^{\rm {E}}\\\vdots \\S_{n}^{\rm {E}}\\\end{bmatrix}}_{1}\dots {\begin{bmatrix}S_{1}^{\rm {E}}\\\vdots \\S_{n}^{\rm {E}}\\\end{bmatrix}}_{m}\end{bmatrix}}&{\text{ Selection function method}}=0{\text{ (User defined)}}\\&&\\{\begin{bmatrix}{\begin{bmatrix}S_{1}^{\rm {E}}\\\zeta _{1}\\\zeta _{2}\\d_{{\rm {p}}1}{\text{ (mm)}}\\\end{bmatrix}}_{1}\dots {\begin{bmatrix}S_{1}^{\rm {E}}\\\zeta _{1}\\\zeta _{2}\\d_{{\rm {p}}1}{\text{ (mm)}}\\\end{bmatrix}}_{m}\end{bmatrix}}&{\text{ Selection function method}}=1{\text{ (Herbst-Fuerstenau)}}\\&&\\{\begin{bmatrix}{\begin{bmatrix}\alpha _{0}\\\alpha _{1}\\\alpha _{2}\\d_{\rm {crit}}{\text{ (mm)}}\\\alpha _{02}\\\alpha _{12}\\\end{bmatrix}}_{1}\dots {\begin{bmatrix}\alpha _{0}\\\alpha _{1}\\\alpha _{2}\\d_{\rm {crit}}{\text{ (mm)}}\\\alpha _{02}\\\alpha _{12}\\\end{bmatrix}}_{m}\end{bmatrix}}&{\text{ Selection function method}}=2{\text{ (Austin)}}\\\end{cases}}$

$Breakage={\begin{cases}{\begin{bmatrix}{\begin{bmatrix}b_{11}&&0\\\vdots &\ddots &\\b_{n1}&\dots &b_{nn}\\\end{bmatrix}}_{1}\\\vdots \\{\begin{bmatrix}b_{11}&&0\\\vdots &\ddots &\\b_{n1}&\dots &b_{nn}\\\end{bmatrix}}_{m}\\\end{bmatrix}}&{\text{ Breakage function method}}=0{\text{ (User defined)}}\\&&\\{\begin{bmatrix}{\begin{bmatrix}\beta _{0}\\\beta _{1}\\\beta _{2}\\\beta _{02}\\\end{bmatrix}}_{1}\dots {\begin{bmatrix}\beta _{0}\\\beta _{1}\\\beta _{2}\\\beta _{02}\\\end{bmatrix}}_{m}\end{bmatrix}}&{\text{ Breakage function method}}=1{\text{ (Austin and Luckie)}}\\&&\\{\begin{bmatrix}{\begin{bmatrix}K\\n_{1}\\n_{2}\\n_{3}\\y_{0}{\text{ (mm)}}\\\end{bmatrix}}_{1}\dots {\begin{bmatrix}K\\n_{1}\\n_{2}\\n_{3}\\y_{0}{\text{ (mm)}}\\\end{bmatrix}}_{m}\end{bmatrix}}&{\text{ Breakage function method}}=2{\text{ (King)}}\\&&\\{\bigg [}\;\;\;{\bigg ]}&{\text{ Breakage function method}}=3{\text{ (Natural selection)}}\\\end{cases}}$