Future low-cost space transportation system analysis

Reliability maximization of a load‐sharing system without redundant components

“…Then, the problem can be written as follows: max 𝑛≥1 𝑅 𝑠 (𝑡; 𝑛) subject to 𝐸 (𝐶; 𝑛) ≤ 𝑐 𝑢 where 𝐸(𝐶; 𝑛) is the expected development cost of a system of 𝑛 components and 𝑐 𝑢 is the maximum available cost. For example, if the power function, 𝐸(𝐶; 𝑛) = 16.6(𝑉 𝑛 ) 0.4 , is fitted to scale the engine development cost in terms of the design thrust value, 28,30 the optimal solution is obtained directly from the Karush-Kuhn-Tucker condition, independently and dependently of the assumed lifetime distribution when using Equations ( 4) and ( 5) to express 𝑅 𝑠 (𝑡; 𝑛), respectively.…”

“…Then, the problem can be written as follows: $$$$\begin{equation}\mathop {\max }\limits_{n \ge 1} {R_s}\left( {t;n} \right)\ {\rm{subject\ \ to}}\ E\left( {C;n} \right) \le {c_u}\end{equation}$$$$where $$E( {C;n} )$$ is the expected development cost of a system of n components and $${c_u}$$ is the maximum available cost. For example, if the power function, $$E ( {C;n} ) = 16.6{( {{V_n}} )^{0.4}},$$ is fitted to scale the engine development cost in terms of the design thrust value, 28,30 the optimal solution is obtained directly from the Karush–Kuhn–Tucker condition, independently and dependently of the assumed lifetime distribution when using Equations () and () to express $${R_s}( {t;n} )$$, respectively.…”