# Does MTBF make any sense?

My wife and I are just wrapping up a two-week trip to New Zealand. As I write this I’m overlooking the lake near Queenstown.

There are parasails floating down from the hill, mountain and road bikers on the trails and roads, trampers, hang-gliders, jet boating, sailing, and bungy jumping – and dozens of other activities occurring.

Not once did any of the brochures talk about MTBF and they shouldn’t. I’m sure some of the activities have a waiver for accidents, etc. yet, most are rather safe.

During the trip, we had two helicopter rides postponed and a kayak trip delayed. The operators maintain an acceptable risk of failure by avoiding bad weather when possible.

The bikes we rented for a day were the best bikes I’ve ever ridden. Good solid equipment, well maintained, along with excellent instruction and trails. (The ride ended at a winery where they picked us and the bikes up for ride back to town).

# MTBF and Vacation Activities

I asked at a bungy jumping site how many jumps the bungy ‘rope’ can last. They said about 2,000 jumps. It was the ‘about’ that was curious. They do count the number of jumps each rope incurs.

They inspect the ropes each day for any signs of wear or damage. And, after 2,000 jumps retire the rope.

I suspect it is not a 2,000 jump MTBF. It wouldn’t make sense to have a totally random failure mode on such equipment. Of course it could happen, yet it has been so rare that it has become an acceptable risk.

Imagine if it was a 2,000 jump MTBF, would you jump? You have a 1 in 2,000 chance that the rope will fail. Not to mention the harness or anchor.

Same for bikes, hang-gliders, kayaks, etc. They all can fail, yet the most likely failure modes are due to use during harsh weather or with poor maintenance or old age.

The equipment I have seen in and around Queenstown is very new, well maintained and very safe. Add a fool and some poor weather and the odds of failure increase.

# MTBF of Accidents

Yes accidents do occur. In bathtubs, along the road, and during adventure activities.

As reliability engineers we probably could calculate the MTBF, if desired.

Would a 1,250,000 shower events per accident make any sense? Would such a number be informative and alter our behavior?

If we really wanted to minimize risks of accidents we’d sell out cars and install non-slip shower stalls.

This leads me to my final point.

# MTBF really doesn’t make much sense

During a vacation, when designing a product or operating of a factory, MTBF really is quite meaningless.

Sure there is a constant and generally unknown probability of failure due to truly random events.

A well done vacation, product design or factory minimizes the chance of random failure. We watch the weather and provide training, for example.

It is the poor or faulty equipment that fails during initial use, or the eventual wear-out that leads to failure. In my experience during this vacation, it is the awareness of wear-out combatted by diligent inspection, excellent maintenance, and retirement that allows so many to enjoy so many adventure activities.

The same for well design products or plants. Those with consideration of initial assembly and shake down, then excellent maintenance and eventual retirement (before failure) works to improve product and equipment usefulness.

I realize that the bungy ropes have maybe another 2,000 or so jumps beyond retirement (an example of safety margin), yet they consider the risk of failure when it becomes ‘real’ as unacceptable.

We should do the same with our designs and plants.

A very good story about the bungy jump. I am thinking—and not jumbing

If we are talking about a constant failure rate, and it was a mbtf on 2000 hours—-and then talking about probability

What is the chance of getting hurt after 1000 jumb

R(1000) = e- ( 1000/2000) = 0,601—–well 40 %—I will still not jumb

(Fred is that the right calculation)

Hi Per,

Thanks for the comment. If you want to know the chance that someone would be hurt in 1000 jumps then your calculation is correct.

If you want to know your chance of getting hurt on the 1001th jump then it’s simply the chance of failure, which is constant at 1 in 2000.

recall that the exponential distribution is memoryless and the chance for failure on the first jump of 5000th is the same (one over MTBF). It is when we tally the combined chances for each jump that we can calculate the chance that a failure occurs or not (reliability).

Cheers,

Fred