A Novel Reason to Use MTBF

Thanks to a reader that noticed my question on why MTBF came into existence, we have a new (new to me at least) rationale for using MTBF. Basically, MTBF provides clarity on the magnitude of a number, because a number in scientific notation is potentially confusing.

What is doubly concerning is the use of MTTF failure rate values in ISO standards dealing with system safety.

Let’s explore the brief email exchange and my thoughts.

First, let me say receiving emails, comments, etc from readers is the highlight of my day. It helps me stay in touch and learn from a wide range of readers. Plus, it is a great way to add more value to my work along the way.

An email arrived that included a nice compliment and quoted my question:

I am not sure why (tend to think it was a marketing decision) someone decided to invert the negative connotation of ‘failures/hour’ into the positive sounding ‘hours/failure’.

Then went on to provide a potential answer:

In Europe we are working with a standard EN ISO 13849 which simplifies safety functions and architectures. If an engineer is not used to calculate with lambda=1E-6 values, than it takes some time to get used. Mainly the mechanical engineer or machinery developer uses MTTF and the standard sets some targets for 30a , 100a etc. I think it is more about not-engineer developer who doesnt want to use exponential numbers and usually at the first sight you dont have a feeling about how big/small an exponential number is.

Overall, this concept of providing a length of an integer is a convenient way to estimate it’s magnitude. This really works well when there are up to about 6 digits. Decerning the different order of magnitudes between a 2 digit number and one with 4 digits is quite easy as one is twice the length of the other.

Large and Small Number Notation

One issue that arises is our inability to quickly decern a 6 and 7 digit number or even more difficult a 9 and 10 digit value.

Scientific notation was in part invented as a convenient way to write very small or very large numbers efficiently. The exponent provides the number of digits or magnitude directly. 2.3E-6 is a small number whereas the number 3.5E-8 is two orders of magnitude smaller.

Here are the two same values converted to MTTF format: 434782.61 and 29411647.71. Which has the lower failure rate? This is a difference between 6 and 8 significant digits and you may have noticed the second number is two digits longer quickly, or maybe not.

Engineering and Numbers

From what I recall and continue to suspect is important, engineers work with numbers. We do calculations. We use formulas. We deal with large and small numbers on a regular basis.

A fundamental understanding of math is a common prerequisite for an engineering sequence of courses.

Making numbers simpler to quickly understand is a great thing, that is why we use scientific notation or other straightforward means to write and use large and small numbers. 0.0000023 becomes 2.3E-6 or 2.3×10-6, which doesn’t manipulate (invert) the number into a large number (6 digits long) instead.

Simplifies Safety Functions and Architectures

This is the most serious concern. Engineers are using an international standard, EN ISO 13849 which ‘simplifies safety functions and architectures’. When our system design require simplication in order to ascertain or design in safety, it just seems wrong to me.

The ability to compare options or quantify safety risk is not facilitated by making that process simpler such that engineers unable to quickly understand large or small numbers by using MTTF.

MTTF is a very poor representation of an item’s time to failure pattern. It masks the nature of the expected or dominant failures tendancy to decrease or increase over time or use. It just uses the average thus losing the often critical information of rate of change over time of the failure rate.

MTTF and MTBF are widely misunderstood and misused.

MTTF or MTBF values used in safety calculations may be provided based on faulty and inaporopiate parts count prediction based methods.

We shouldn’t use (never, never ever) MTTF or MTBF to describe or estimate reliability performance and expecailly not for safety design and operation considerations.

Do the math. Understand the failrue mechanisms and thier chaning rates of occurance over time or use. Let’s not under or over estimate safety risks based on ‘simplied’ methods to deal with small or large numbers.