There are many ways and methods used in estimating reliability of products or software. Many products have their reliability expressed as Mean Time Between Failures (MTBF), which is the expected mean or average time in which the product will fail. In Semiconductors the measure frequently used is Failures In Time (FIT).
Quoted reliability numbers are not a guarantee that the product will last that long. Some products will fail in much shorter periods and others may last far longer. All that goes into establishing the average. The average rates that a supplier may quote are calculated and represent an estimate. They aren’t proven because the length of time to prove them would take too long and would extend longer than the product’s normal sales life cycle. For things like electrical components you can easily have product MTBF's of 100,000 hours or more. That is something like 11.4 years.Supplier warranties may be anywhere between 1 and 3 years, seldom more unless the market demands it.
Unless you can prove that there was a deliberate misrepresentation by the Supplier about the product and its reliability, the only responsibilities the Supplier will have to the Buyer for reliability is what was committed in the sales agreement under the warranty. Quality, reliability, and functionality of the product are all issues fall under the product warranty. The only time a supplier is going to be responsible to provide repair or replacement for any of them is if they fail to meet the agreed specification during the warranty term. Even then the supplier will only have responsibility if the cause for the product being defective is not excluded by a warranty exclusion.
The one exception with regards to reliability is when the parties negotiate what's called an "Epidemic Defects" clause. Epidemic defects clauses usually have coverage that extends beyond the warranty period. In those situations Supplier has additional obligations if certain events occur that would make it an epidemic defect. In epidemic defect provisions the supplier may be responsible for not just the replacement of the defective product but they may also assume some of the buyer’s additional costs associated with having to replace the defective items. As these type of clauses provide substantial increased potential risk and cost to the supplier they will want the definition of what constitute an epidemic defect to be very narrow. They won’t agree that all defects that may affect the product’s reliability will count. They may agree upon a measurement that requires a threshold or percentage of defects for the same root cause to occur for it to be considered epidemic.
Reliability does have a connection to another area of contracts. If the defect in the product causes a safety problem or causes personal injury or property damage other terms come into play. In most contracts in addition to the warranty against defects in material and workmanship there will also be other warranties that apply - the product is safe, the product complies with applicable laws etc.
The warranty against defects in materials and workmanship must survive the expiration of the contract so you get the benefits of that warranty and can get defective material repaired or replaced under the warranty. Those other warranties and indemnities against 3rd party claims for personal injury need to survive and be open ended as to their term. The reason for that is because potential third party claims are not extinguished when the warranty has expired. They are only extinguished when the period for filing a claim has lapsed under the applicable statute of limitations for that jurisdiction. For example in New York, an injured party has six years after they were injured to initiate a personal injury claim.
Many times problems with product safety may also be classified as an epidemic defect and require the supplier to replace those items. In those cases the Supplier isn't committing to replace them because they didn't meet their reliability goal, they are doing it because unsafe products represent potential product liability claims that could cost far more than the cost of replacing the product.They will also do that because in most well written contracts both the warranties for a product being safe and indemnifications against third party claims for product liability will also survive the expiration of the contract where all those costs will be their costs.