Some many years ago I ran across a data sheet for a cooling fan (used to cool a desktop computer, for example) that listed the fan’s life as **50,000 hours MTBF. **The big bold lettering was on the data sheet and was the only use of bold on the entire data sheet. One couldn’t miss it. The computers we used these fans within had a one year warranty, plus were expected to operate for a home computer user for about 5 years. Thus, we would expect the fan to also operate for five years without failure.

The chassis designer selected the fan model with the assistance of the component engineer, and both believed the 50,000 hours MTBF would be more than adequate for the computer application. For those that routinely read this blog, you already know the rest of the story, so let’s see if we agree. For new readers, I trust the remainder of the post is not new information for you. At least I hope not.

One of the first pieces of information we need is how often we expect the fan to operate. The design team expected the home user to keep the system powered on and actively operating up to 16 hours per day (heavy use by home business or game playing). To be conservative they rounded up to 24 hours of use per day related to the fan. That would be about 8760 hours of use per year, or 43,800 hours of use in five years.

Another element of information we should consider the reliability goal for the computer and specifically the goal for the fan. A short discussion with the program manager revealed a desire to achieve at least 95% reliability for the overall computer and the fan alone should be at least 99% reliable over the first year. For five years, the computer expected 85% reliability and the fan at least 95% reliability. Those were the goals.

NOTE: I’m not going to discuss that MTBF assumes a constant failure rate, and fans generally fail due to bearing failure due to wear out, and the inappropriate fan testing by the vendor to generate the MTBF value. Let’s just take the information we have, and move on.

Given, 50k hrs MTBF for the fan and an expected use of 8,760 hrs per year, what is the reliability (probability of success) just for the fan at one year. To calculate this result, use the reliability function of the exponential distribution.

$latex R(t)={{e}^{-\frac{t}{\theta }}}$

Where t is time in hours and theta is MTBF also in hours. R(t) is the probability of not failing over time period t. 8760 divided by 50,000 is 0.1572. Negative sign and exponent, to find R(8,760) = 83.9% Which means about 16% of fans are expected to fail within one year.

Well, this fan alone is expected to consume the entire budget and more. It’s even worse for five years. R(5*8,760) = 41.6% or over half of the fans are expected to fail within five years.

The component engineer was shocked. “50k hrs is longer than 5 years, so it should be good and not have any failures”, he said. The design engineer said, smiling as he thought a way around this dilemma, “Ah, remember we are being conservative in the use time by assuming 24 hr a day operation. In reality, the fan probably runs no more than 12 hours per day.”

Ok. Let’s run the numbers using 12 hours per day. 5 * 8,760 /2 is 21,900 hours of use in five years. And R(21,900) = 64.5%, which is still not good enough. And, one year, R(4,380) = 91.6%, and is still not good enough.

Assuming the reported value of 50,000 hours MTBF and the use of MTBF is correct for the fan in question, and even cutting the expected use time, it’s still not reliable for this application. Time to find another fan or cooling solution.

In general, when you see the use of MTBF on a data sheet, that is a wonderful indicator to ask more questions. How was the number generated, what testing supports the conclusion, how was the testing done, what conditions, and how will this number relate to our use conditions and duration expectations? Just a little math is often enough to start the process going, then its good engineering to design the right solution that meets the reliability goals.