cbm-rbd-rstarfigs.tex

\documentclass[authoryear]{elsarticle}

% ------------ packages -------------

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\usepackage{amsmath}
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\usepackage[usenames,dvipsnames]{xcolor}
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\usepackage{url}
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%\usepackage{hyperref}
%\usepackage[bookmarks]{hyperref}
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% ------------ custom defs -------------

\newcommand{\reals}{\mathbb{R}}
\newcommand{\posreals}{\reals_{>0}}
\newcommand{\posrealszero}{\reals_{\ge 0}}
\newcommand{\naturals}{\mathbb{N}}

\newcommand{\dd}{\,\mathrm{d}}

\newcommand{\mbf}[1]{\mathbf{#1}}
\newcommand{\bs}[1]{\boldsymbol{#1}}
\renewcommand{\vec}[1]{{\bm#1}}

\newcommand{\uz}{^{(0)}} % upper zero
\newcommand{\un}{^{(n)}} % upper n
\newcommand{\ui}{^{(i)}} % upper i

\newcommand{\ul}[1]{\underline{#1}}
\newcommand{\ol}[1]{\overline{#1}}

\newcommand{\Tsys}{T_\text{sys}}

\newcommand{\Rsys}{R_\text{sys}}
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\newcommand{\uRsys}{\ol{R}_\text{sys}}

\newcommand{\fsys}{f_\text{sys}}
\newcommand{\Fsys}{F_\text{sys}}
\newcommand{\lFsys}{\ul{F}_\text{sys}}
\newcommand{\uFsys}{\ol{F}_\text{sys}}

\newcommand{\lgt}{\ul{g}}
\newcommand{\ugt}{\ol{g}}

\newcommand{\E}{\operatorname{E}}
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\newcommand{\wei}{\operatorname{Wei}} % Weibull Distribution
\newcommand{\ig}{\operatorname{IG}}   % Inverse Gamma Distribution

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%\def\yi{y\ui}
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\def\yiu{\ol{y}\ui}

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\def\ykzu{\ol{y}\uz_k}
\def\yknl{\ul{y}\un_k}
\def\yknu{\ol{y}\un_k}

\newcommand{\ykzfun}[1]{y\uz_{#1}}
\newcommand{\ykzlfun}[1]{\ul{y}\uz_{#1}}
\newcommand{\ykzufun}[1]{\ol{y}\uz_{#1}}


\def\nz{n\uz}
\def\nn{n\un}
%\def\ni{n\ui}
\newcommand{\nfun}[1]{n^{({#1})}}
\newcommand{\nfunl}[1]{\ul{n}^{({#1})}}
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\def\nzl{\ul{n}\uz}
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\def\nkzl{\ul{n}\uz_k}
\def\nkzu{\ol{n}\uz_k}
\def\nknl{\ul{n}\un_k}
\def\nknu{\ol{n}\un_k}

\def\yknow{y_k^{(\tnow)}}
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\def\tautk{\tau(\vec{t}_k)}

\def\MZ{\mathcal{M}\uz}
\def\MN{\mathcal{M}\un}

\def\MkZ{\mathcal{M}\uz_k}
\def\MkN{\mathcal{M}\un_k}

\def\PkZ{\Pi\uz_k}
\def\PkN{\Pi\un_k}
\newcommand{\PZi}[1]{\Pi\uz_{#1}}

\def\tnow{t_\text{now}}
\def\tpnow{t^+_\text{now}}

\newcommand{\Rsysnow}{R^{(t_\text{now})}_\text{sys}}
\newcommand{\Tsysnow}{T^{(t_\text{now})}_\text{sys}}
\newcommand{\tsysnow}{t^{(t_\text{now})}_\text{sys}}
\newcommand{\fsysnow}{f^{(t_\text{now})}_\text{sys}}
\def\eknow{e_k^{(\tnow)}}
\def\cknow{c_k^{(\tnow)}}
\def\vectknow{\vec{t}_k^{(\tnow)}}
\def\Phinow{\Phi^{(\tnow)}}
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% ------------ options -------------

\allowdisplaybreaks

\journal{RESS}

\begin{document}

%\section{Prospective cost rate}

\begin{figure}
\includegraphics[height=0.4\textheight]{tauhist2fig3R}
\caption{Failure history with failures more or less \textbf{like expected},
$\tausnow$ based on \textbf{prospective cost rate}.
Reliability function value at cost-optimal moment of maintenance in lower right panel.
This decreases from initial value $0.942$;
over time, we increasingly risk a system failure to get prospective-optimal costs,
and these costs go up.}
\label{fig:tauhist2fig3R}
\end{figure}

\begin{figure}
\includegraphics[height=0.4\textheight]{tauhist2fig3TR}
\caption{Failure history with failures more or less \textbf{like expected},
$\tausnow$ based on \textbf{total cost rate}.
Reliability function value at cost-optimal moment of maintenance in lower right panel,
incrieasing from intial value;
with total cost, we risk less and less over time, and $\tausnow$ tends to $0$.}
\label{fig:tauhist2fig3TR}
\end{figure}

\begin{figure}
\includegraphics[height=0.4\textheight]{tauhist1fig3R}
\caption{Failure history with failures \textbf{later than expected},
$\tausnow$ based on \textbf{prospective cost rate}.
Reliability function value at cost-optimal moment of maintenance in lower right panel,
decreasing from initial value $0.942$.
Zig-zag is probably due to limited resolution for $\tausnow$ (0.01) and $\tnow$ grid (0.1).}
\label{fig:tauhist1fig3R}
\end{figure}

\begin{figure}
\includegraphics[height=0.4\textheight]{tauhist1fig3TR}
\caption{Failure history with failures \textbf{later than expected},
$\tausnow$ based on \textbf{total cost rate}.
Reliability function value at cost-optimal moment of maintenance in lower right panel.}
\label{fig:tauhist1fig3TR}
\end{figure}

\begin{figure}
\includegraphics[height=0.4\textheight]{tauhist4fig3R}
\caption{Failure history with failures \textbf{earlier than expected},
$\tausnow$ based on \textbf{prospective cost rate}.
Reliability function value at cost-optimal moment of maintenance in lower right panel,
decreasing from initial value $0.942$.
Zig-zag is probably due to limited resolution for $\tausnow$ (0.01) and $\tnow$ grid (0.1).}
\label{fig:tauhist4fig3R}
\end{figure}

\begin{figure}
\includegraphics[height=0.4\textheight]{tauhist4fig3TR}
\caption{Failure history with failures \textbf{earlier than expected},
$\tausnow$ based on \textbf{total cost rate}.
Reliability function value at cost-optimal moment of maintenance in lower right panel.}
\label{fig:tauhist4fig3TR}
\end{figure}

\end{document}