Here's how you can effectively communicate the impact of software bugs on project timelines and budgets.

The first step is to assess the bug's severity. This is sometimes called triaging the issue. Does this bug compromise security? Or, is data loss involved? If the answer to either is yes, this is immediately a priority 1 critical bug. If the answer to both of these is no, then severity and priority must be determined accordingly. Is this an inconvenience and there's a workaround for the end user? Then maybe an immediate fix is not as urgent.

Time impact must be communicated to the engineers. Bugs discovered during development always take less time to correct. Finding them in QA and then production increases the time cost significantly. THIS IS WHY THE MOST IMPORTANT QA TESTING SHOULD BE DONE BY DEVELOPERS, NOT QA! DevQual, the process of an engineer testing their own code, and Peer Review, the process of having another (senior) engineer review the code before a merge, are critical. Companies that forego these two processes handicap themselves in the long run. The time spent on these two processes is much less than the time spent fixing bugs found in production. An ounce of prevention is worth a pound of cure.

One thing to consider is that stakeholders may have a tendency to underestimate infrastructure improvement, so it's a part of the developers' job to share the benefits of doing so in order to get the necessary time to do it. All companies may suffer from bugs, but having well established steps of analysis, briefing, tests and reviews are some examples of processes to implement on your team to prevent those situations. It's common to see it all fall on the shoulders of the dev team, but there might a good chance that there was some miscommunication in the process that was ignored and passed through. For that, it's important that those steps aren't looked at just once, but instead they get constantly assured in a multi-layered process.