What's Wrong with MTBF
The use of MTBF (Mean Time Between Failures) is almost always applied wrong. As a producer of a product you would want the product to last beyond the warranty period and long enough to be perceived by the customer as a 'Quality' product. One way of quantifying this is that a product will have X% reliability at Y years with C% confidence.
MTBF is the inverse of the failure rate, NOT the life-time of the product. As example a product or assembly might have a MTBF of 400,000 device-hrs. This does not mean the product life is 400,000hrs (45.6 years)! It means the failure rate is 2.5 per million hours.
Bathtub Curve
Implicit in the concept of MTBF or it's inverse failure rate is the that the failure rate is constant. Think of the MTBF as meaning that in any given hour the possibility of failure is 1/MTBF. This is applicable during the flat portion of the 'Bathtub' curve showing failure rate versus time (see figure). Quite often in a product there will be components that have a very low failure rate but have a wear out function that forms the right-hand side of the Bath Tub curve. For example, the product with a 400,000 device-hr MTBF might have a element that wears out at 20,000hrs as example.
One way of analyzing a product is to add up all the failure rates of the individual components. Commonly expressed as failures per billion hours this is referred to as the FIT rate (Failures in Time). For our example a product with a MTBF of 400,000 has a FIT rate of 2500.
Back to our example, a product with an MTBF of 400,000 that is operated 24/7 will have a failure rate of about (1 - exp(-t/MTBF)) in a year, or 2.2% annual failure rate (AFR). Because of the uniform distribution of failures a small sample of the failure rate may result in measured values ranging from 1% to 5%, but over a large population will be 2.2%. In 5 years this would be over 10% failures, or less than 90% reliability. In this light the MTBF of 400,000 no longer seems so good.
Design for Reliability
When designing a product from the start there should be a reliability target and a pro-forma reliability budget based on the target design. If the reliability target looks like it cannot be met then the architecture of the system needs to be re-thought out or the reliability target changed, understanding the business consequences.