stage number = i

There are 5 stages (panel locations 1 to 5).

decision variables = t_i

Thickness for panel i

state variable at stage i = s_i

Overall reliability ( $\ge r_1$ ) required for the remaining stages i, i + 1, …, 5 presenting restrictions on future decisions

return function at stage i = g(s_i, t_i)

Weight of panel i for a fixed remaining reliability s_i and thickness for this s_i

state transformations

$s_{i+1}=\frac{s_i}{r\left(t_i\right)},i=1,2,3,4$

recursive equations

$\begin{array}{l}{f}_i\left(s_i\right)=\underset{t_i}{\min }\left[g\left(s_i,t_i\right)+f_{i+1}\left(\frac{s_i}{r\left(t_i\right)}\right)\right],i=1,2,3,4\\ f_5\left(s_5\right)=\underset{t_5}{\min }g\left(s_5,t_5\right)\end{array}$