TL;DR
They have decided that if there are any User Stories not fully completed (as per the DoD) at the end of the Sprint, the Sprint has failed.
This is not only incorrect, it's an abuse of the Scrum framework and a thorough misunderstanding of how work is selected for inclusion into a Sprint.
The purpose of a Sprint is not to complete user stories. That's simply a means to an end. Rather, the purpose of a Sprint is to provide a time-box to work on Product Backlog items that collectively deliver the value defined by an overarching Sprint Goal.
Sprint Failure Conditions
While not addressed specifically within The Scrum Guide, a Sprint really has only three failure conditions:
- The Sprint Goal has not been met.
- The delivered Increment is not in usable condition.
- The Increment does not meet the "Definition of Done."
That's it. Individual stories can be done or not-done, forecasts (estimates) can be missed, and the team may have successfully delivered the wrong MacGuffin. Such Sprints are still technically "successful" in that they delivered a potentially-releasable Increment and leveraged the framework to provide the business with process transparency and appropriate opportunities to inspect-and-adapt.
Sprint Goals and Increments
The following elements of the Scrum framework are explicitly defined in The Scrum Guide. The Sprint Goal is developed during Sprint Planning, and provides guidance throughout the Sprint. The Increment is the work completed according to the Definition of Done, and is essentially the de facto deliverable for the Sprint.
Sprint Goal
The selected Product Backlog items deliver one coherent function, which can be the Sprint Goal. The Sprint Goal can be any other coherence that causes the Development Team to work together rather than on separate initiatives.
Increment
At the end of a Sprint, the new Increment must be “Done,” which means it must be in useable condition and meet the Scrum Team’s definition of “Done.” It must be in useable condition regardless of whether the Product Owner decides to actually release it.
Educational Opportunities
In general, your management team's approach is exhibiting a number of smells that indicate a faulty Scrum implementation. It is the Scrum Master's job to educate the entire organization, including the Scrum Team and senior management, about the way Scrum actually works.
Specifically, you should use this as an opportunity to address the following project smells implied by your original post:
A Sprint should have a coherent goal.
As defined by the Scrum Guide, each Sprint should have a defined goal which causes the team to work together rather than on separate initiatives. If you don't have a coherent Sprint Goal, a coherent Increment, or a collection of Sprint Backlog Items that are interrelated, then the framework is being implemented incorrectly.
Work is selected by the Scrum Team, not assigned from the outside.
The Product Owner prioritizes work on the Product Backlog, and the team negotiates with the Product Owner during Sprint Planning to select stories for the Sprint Backlog that will:
- Fit within the time box.
- Support the Sprint Goal.
- Collectively deliver a vertical slice of value.
Assigning stories to the team, selecting unrelated stories, or failing to leverage the "team" aspect of the Development Team when performing Sprint Planning are all huge red flags.
Forecasts are not money-back guarantees.
Sprint Planning is a short-term planning exercise that estimates both level-of-effort and team capacity to arrive at a reasonable forecast of the work that can be completed within a given time box (the Sprint) with the resources and knowledge currently available. Forecasts can be missed for a wide variety of reasons; it is not inherently a failure of either the framework or the team's work during the iteration. Instead, a missed forecast is an opportunity to:
- Learn more about the problem domain.
- Inspect-and-adapt the framework or development process.
- Improve estimating techniques.
It is more effective to iterate rather than to affix blame.
If your organization is trying to "hold people accountable" for forecasts, they have misunderstood the difference between an estimate and a guarantee. Educate them about how iterative development and iterative process improvement actually work, and explain how the Scrum framework provides them with the tools they need to effectively manage emergent designs and processes.