For low-cost disposable products, working "most of the time" may suffice. For other products, different rules apply. An automobile that starts most of the time may not generate much customer loyalty. Your customers have expectations of performance.
While not always right, customers have all the money. If the first rule of business is to stay in business, you want to keep customers happy. Unreliable products make this more difficult. Years ago, I came to the obvious conclusion that we couldn't make money on warranty repairs. No one liked my idea of a 30-second warranty, so I had to design products that wouldn't break. (Real reason: I hated fixing things.)
A product that doesn't break requires paying close attention to specifications for each component, and taking some specs with a very large grain of salt. "Typical" specs usually look pretty good. Min and max specs show up in smaller print, on page 4. The latter specs generally come from engineering, and may indicate what the component will do, under some circumstances.
"Typical" specs should represent the middle of the distribution curve, but usually reflect what marketing thinks will sell more parts. A wise engineer once told me how marketing thinks: "Since customers always ask for ten times what they need, spec the part at ten times what it will do." Restrict your design efforts to designing for typical specs and you'll get a product that works "most of the time."
Min/max analysis takes time. Simulation usually doesn't help. FEA depends on input models, based on "typical" specs. Garbage in, etc. As one expert said, "In theory, practice and theory are the same. In practice, they are not." It's far easier to design with typical specs. You have only one set of numbers and they look good. The Law of Prototyping guarantees proper first unit operation: "Even with a blindfold, you will pull the highest performing and best-matched parts from inventory." But, manufacturing will get parts from opposite ends of the distribution curve. Tolerances will accumulate in the worst possible direction on the product you ship to your highest profile customer. Without adequate margins, the product will fail, their plant will shut down, and they will post an opinion on their website that your parents never took a vow of marriage. But you finished the design on time, and field service can fix the problem.
As usual you have trade-offs. Ship a thousand widgets, fifteen come back, costing twenty bucks apiece to fix. You can't justify more than thirty cents of additional cost per widget, and probably less, since you won't eliminate all returns. If you ship one big widget and have to send three people out to fix it under warranty, it can cost thousands. Most companies put manufacturing and service/repair in separate cost centers. Manuacturing wants its numbers to look good, even (or especially) at the expense of other departments, and will shun extra costs. You have to look at the total picture. It takes enlightened management (stop laughing) to realize this—and to support design to min/max specs.
You acquire knowledge in school. You achieve wisdom when you discover that Murphy supercedes Newton, Maxwell, and Einstein. You find enlightenment when you realize that Murphy, who would have designed to typical specs, was an optimist.