# MTBF as stepping stone to better reliability metrics

MTBF is taught in many textbooks and introductory reliability courses. There may be some mention of Weibull and other distributions. You may even learn about the four functions: – reliability – probability density function (PDF) – cumulative density function (CDF) – hazard function

Plus, you learn a bit about risk analysis, modeling, prediction, environmental and life testing, and field data analysis. Plus, other topics including design for reliability, physics of failure, and prognostic health management.

Most often, in my experience, after a quick mention of the four functions, we rarely ever see them again. The examples tend to use MTBF (or MTTF) directly and not the appropriate function as a function of time.

Why?

## Possible Reasons Why

I’m not exactly sure and do have a few hypothesis though

- It’s easy. MTBF simplifies the reliability statistics and math involved with reliability engineering tools such as predictions, modeling, testing and data analysis. Maybe the idea is to provide an introduction to the breadth of tools in the field without having to become a solely a reliability statistics class.
- No body likes statistics anyway. Even statistics (not the subset of reliability statistics) is considered tough. In many classes I teach I ask about the groups knowledge and use of basic, advanced and reliability statistics. Most are in the ‘had that class and have avoided statistics ever since’ camp. So, the thought is to encourage the use of reliability tools keep the statistics simple.
- The instructor doesn’t know the necessary reliability statistics. With so many classes, references and the wide-spread use of MTBF, why bother with anything else. Also, I would suspect that some instructors don’t know reliability statistics beyond MTBF for some combination of the above two reasons. They don’t know it, so don’t teach it other in passing.
- It’s what sells or is being asked to provide. This relies on the notion that the customer is always right. So, if you the instructor or author knows MTBF only a simplification, they don’t teach or write about other methods since that wasn’t requested. If the customer has only ever seen and used MTBF, they most likely are ignorant of other metrics or methods.

There may be other reasons. You get the idea.

## Intention and Motivation Around Moving to Other Metrics

One of the most common responses to the NoMTBF site and presentations, is: “What would I use instead?”

I always respond with, “Reliability, the probability of successful operation over a specified time period in a specified environment.” It’s the definition of reliability.

The probability part is what trips up many though. I get that.

## Missing stepping stones

If the class uses MTBF out of convenience and mentions the world of distributions and functions, and we find the widespread use of MTBF. Maybe just mentioning alternatives to MTBF isn’t enough.

It would be great if everyone learning about reliability would master the statistics. That’s not likely to happen given the lack of time & funding for additional time in classes, plus the general avoidance most have for stats.

Maybe we are missing a few stepping stones that would help bridge the gap between only using MTBF and doing the math. Maybe the leap is currently seen as too far and too risky.

One idea of a stepping stone for repairable systems is the Mean Cumulative Function (MCF) plot. It is a plot of time along the x-axis and the cumulative count of failures on the y-axis. When a failures occurs for a single system, for that time mark increment the line up one step. Eventually, with more failures, the graph appears like staircase although sometimes with long and short step s or landings.

The MCF plot is visual, often tells a story, and is both easy to construct and interpret.

Another stepping stone, this time for non-repairable systems, is the manual (or with a spreadsheet) creation of a Weibull or Lognormal fit of the time to failure data. Like the MCF, these are relatively easy to create, are visual, and easy to interpret. The fitting parameters provide a means to actually use the associated functions for the distribution to answer questions such as: – how many failures should we expect next month – what is the early life or warranty period failure rates (using field data) – what is the chance of failure during the next month

I’m sure there are other candidate intermittent stepping stones. The idea is we need to create and advocate the use of basic statistical tools. Once those only using MTBF land on a step like MCF or CDF plots, they find

- the ability to make better decisions
- their analysis is more accurate than using MTBF
- they are perceived as the statistics expert on campus
- and, you may find that this irrational fear of statistics has been unfounded. It’s fun (and useful) after all.