There are several ways to add a frame around such elements (note that bounding box and box in general do mean something else with LaTeX, i.e. do not imply a drawn line).
The simplest way is to use the adjustbox
package:
\documentclass{IEEEtran}
\usepackage{subfigure}
\usepackage{adjustbox}
\usepackage{blindtext}% for dummy text only
\begin{document}
\blindtext
\begin{figure}[htp]
\begin{adjustbox}{varwidth=\textwidth,fbox,center}
\subfigure[Process with no error]{\label{noerror}\includegraphics[width=1.5in]{example-image-a}}
\subfigure[Process with syntactic errors (connector having multiple incoming edges and presence of hanging node)]{\label{synerror}\includegraphics[width=1.5in]{example-image-b}} \\
\subfigure[Process with deadlock]{\label{deadlock}\includegraphics[width=1.5in]{example-image-c}}
\subfigure[Process with lack of synchronization]{\label{lacksync}\includegraphics[width=1.5in]{example-image}}
\end{adjustbox}
\caption{Different kinds of errors occuring in InFlux Processes}
\label{processes}
%\vspace*{-0.65cm}
\end{figure}
\blindtext
\end{document}

You can also use varwidth
and \fbox{..}
directly to avoid the need for an extra package:
\documentclass{IEEEtran}
\usepackage{subfigure}
\usepackage{graphicx}
\usepackage{varwidth}
\usepackage{blindtext}% for dummy text only
\begin{document}
\blindtext
\begin{figure}[htp]
\centering
\fbox{\begin{varwidth}{\textwidth}
\subfigure[Process with no error]{\label{noerror}\includegraphics[width=1.5in]{example-image-a}}
\subfigure[Process with syntactic errors (connector having multiple incoming edges and presence of hanging node)]{\label{synerror}\includegraphics[width=1.5in]{example-image-b}} \\
\subfigure[Process with deadlock]{\label{deadlock}\includegraphics[width=1.5in]{example-image-c}}
\subfigure[Process with lack of synchronization]{\label{lacksync}\includegraphics[width=1.5in]{example-image}}
\end{varwidth}}
\caption{Different kinds of errors occuring in InFlux Processes}
\label{processes}
%\vspace*{-0.65cm}
\end{figure}
\blindtext
\end{document}
Finally, you can also avoid the varwidth
package if you are willing to calculate the required width yourself. Then you can use minipage
directly.
This is needed in order to box the content for the frame while still allowing for line breaks:
\documentclass{IEEEtran}
\usepackage{subfigure}
\usepackage{graphicx}
\usepackage{blindtext}% for dummy text only
\begin{document}
\blindtext
\begin{figure}[htp]
\centering
\fbox{\begin{minipage}{3.05in}%
\subfigure[Process with no error]{\label{noerror}\includegraphics[width=1.5in]{example-image-a}}
\subfigure[Process with syntactic errors (connector having multiple incoming edges and presence of hanging node)]{\label{synerror}\includegraphics[width=1.5in]{example-image-b}} \\
\subfigure[Process with deadlock]{\label{deadlock}\includegraphics[width=1.5in]{example-image-c}}
\subfigure[Process with lack of synchronization]{\label{lacksync}\includegraphics[width=1.5in]{example-image}}
\end{minipage}}
\caption{Different kinds of errors occuring in InFlux Processes}
\label{processes}
%\vspace*{-0.65cm}
\end{figure}
\blindtext
\end{document}
There are also other packages for this, e.g. mdframed
.
tcolorbox
orframed
.\centering
instead ofcenter
.