I would immediately challenge your conclusion that "processes were not followed" due to resource limitations in either numbers or expertise. It does not require numbers or expertise to follow a process. It requires rules, discipline, and leadership / management.
But to answer your question, risk management is the process and analytical tool to understand and do something about your estimates and human resources threats.
The term shortage of resources implies there is a number of staff at which the task is perfectly sized--that is, one less and the task has a shortage issue. In fact, there is a range of resources--or cost and schedule--that more represents the degree of risk and likelihood of success.
Unfortunately, during estimation, we too often use a deterministic approach--a single point--to estimate. That is, we look at a task and say it will take six people. The true estimate, however, might be four to nine people and six may represent the 40th percentile or so. Understanding the true non deterministic estimate is the key to understanding your risk. This will allow you to derive mitigating strategies, such as strong process control :), to maximize your chances and to put away some contingent funds to bring in additional folks if you need it. This, by the way, is an organic project risk.
Risk management is also the tool with which you understand your discrete human resource risks. Humans are terribly unreliable and suffer from severe performance variation. Further, while your target might be six resources but you can find only four, or you find six but skill sets with a proven record are unavailable or you cannot afford them. Tons of scenarios but here again, risk management will allow you to identify what these threats are and what to do about them.