\documentclass{standalone}
\usepackage{tikz}
\usepackage{siltex}
\usetikzlibrary {arrows.meta,positioning,calc,math}
\tikzset{nodes={text height=.7em, text width=2.6cm, align=center,
draw=black!50, thick, font=\footnotesize, fill=white},
>={Stealth[round,sep]}, rounded corners, thick}

\pgfdeclarelayer{bg}
\pgfsetlayers{bg,main}

\begin{document}
    \begin{tikzpicture}[on grid,y=1.1cm,x=2.9cm]
        \input{graphics/design_flow.tikz}
    \def\myphasegroup(#1,#2,#3){%
        \begin{scope}[nodes={draw=none, fill=none,text height={}}]
            \coordinate (a) at ($(#1.north west)+(\rectoffset)+(0mm,2.5mm)$){};
            \coordinate (b) at ($(#2.south east)-(\rectoffset)-(\rectoffsetleft)$){};
            \draw[fill=lightgray] (a) rectangle (b);
            \node[anchor=center] at ($(#1)+(\textoffset)+(0mm,4mm)$) {#3};
        \end{scope}
    };
        \begin{pgfonlayer}{bg}
            %\phasegroup(pd,id,Systems Engineering);
            \myphasegroup(ss,rd,Development Cycle)
        \end{pgfonlayer}
    \end{tikzpicture}
\end{document}