I am looking for a verb meaning "to make something more robust", especially in a software engineering context.
Is "to robust" correct and understandable? "Robustify" seems to be another candidate but does not seem so common.
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Neither robustify nor 'to robust' are correct.
You can use 'to make robust' or any of the options Bob noted.
I would use "strengthen", "fortify", or "harden", although "harden" has a distinct security meaning.
bolster: v. Support or strengthen; prop up: "the fall in interest rates is starting to bolster confidence".
For example, "You will help refactor the code and bolster the test suite."
There's no single word to describe making software more robust. Some ways of making software more robust are: simplify, debug, re-factor (especially functional decomposition and code re-use), make the interface more user friendly, make the program resilient to input errors and even recover from some runtime errors, etc.
"Harden" comes to mind, as in hardening a computer system. See https://en.wikipedia.org/wiki/Hardening_(computing)
Robustification (n.)-- the process by which, or the act of, making a procedure or algorithm (esp. in engineering, software or statistics) less susceptible to uncertainty.
See also robustify (v.)
"Enhence Robustness" might be what you want. I saw it in the title of a nature article("Enhancing robustness of interdependent network under recovery based on a two-layer-protection strategy").
Sometimes I use to mature when I need a verb, such as in process descriptions.