## ISO 13849-1 Analysis — Part 4: MTTFD – Mean Time to Dangerous Failure

This entry is part 4 of 6 in the series How to do a 13849-1 analysis

Functional safety is all about the likelihood of a safety system failing to operate when you need it. Understanding Mean Time to Dangerous Failure, or MTTFD, is critical. If you have been reading about this topic at all, you may notice that I am abbreviating Mean Time to Dangerous Failure with all capital letters. Using MTTFD is a recent change that occurred in the third edition of ISO 13849-1, published in 2015. In the first and second editions, the correct abbreviation was MTTFd. Onward!

If you missed the third instalment in this series, you can read it here.

## Defining MTTFD

Let’s start by having a look at some key definitions. Looking at [1, Cl. 3], you will find:

3.1.1 safety–related part of a control system (SRP/CS)—part of a control system that responds to safety-related input signals and generates safety-related
output signals

Note 1 to entry: The combined safety-related parts of a control system start at the point where the safety-related input signals are initiated (including, for example, the actuating cam and the roller of the position switch) and end at the output of the power control elements (including, for example, the main contacts of a contactor)

Note 2 to entry: If monitoring systems are used for diagnostics, they are also considered as SRP/CS.

3.1.5 dangerous failure—failure which has the potential to put the SRP/CS in a hazardous or fail-to-function state

Note 1 to entry: Whether or not the potential is realized can depend on the channel architecture of the system;
in redundant systems a dangerous hardware failure is less likely to lead to the overall dangerous or fail-tofunction
state.

Note 2 to entry: [SOURCE: IEC 61508–4, 3.6.7, modified.]

3.1.25 mean time to dangerous failure (MTTFD)—expectation of the mean time to dangerous failure

Definition 3.1.5 is pretty helpful, but definition 3.1.25 is, well, not much of a definition. Let’s look at this another way.

## Failures and Faults

Since everything can and will eventually fail to perform the way we expect it to, we know that everything has a failure rate because everything takes some time to fail. Granted that this time may be very short, like the first time the unit is turned on, or it may be very long, sometimes hundreds of years. Remember that because this is a rate, it is something that occurs over time. It is also important to be clear that we are talking about failures and not faults. Reading from [1]:

3.1.3 fault—state of an item characterized by the inability to perform a required function, excluding the inability during preventive maintenance or other planned actions, or due to lack of external resources

Note 1 to entry: A fault is often the result of a failure of the item itself, but may exist without prior failure.

Note 2 to entry: In this part of ISO 13849, “fault” means random fault.
[SOURCE: IEC 60050?191:1990, 05-01.]

3.1.4 failure— termination of the ability of an item to perform a required function

Note 1 to entry: After a failure, the item has a fault.

Note 2 to entry: “Failure” is an event, as distinguished from “fault”, which is a state.

Note 3 to entry: The concept as defined does not apply to items consisting of software only.

Note 4 to entry: Failures which only affect the availability of the process under control are outside of the scope of this part of ISO 13849.
[SOURCE: IEC 60050–191:1990, 04-01.]

3.1.4 Note 2 is the important one at this point in the discussion.

Now, where we have multiples of something, like relays, valves, or safety systems, we now have a population of identical items, each of which will eventually fail at some point. We can count those failures as they occur and tally them up, and we can graph how many failures we get in the population over time. If this is starting to sound suspiciously like statistics to you, that is because it is.

OK, so let’s look at the kinds of failures that occur in that population. Some failures will result in a “safe” state, e.g., a relay failing with all poles open, and some will fail in a potentially “dangerous” state, like a normally closed valve developing a significant leak. If we tally up all the failures that occur, and then tally the number of “safe” failures and the number of “dangerous” failures in that population, we now have some very useful information.

The different kinds of failures are signified using the lowercase Greek letter $\lambda$ (lambda). We can add some subscripts to help identify what kinds of failures we are talking about. The common variable designations used are [14]:

$\lambda$ = failures
$\lambda_{(t)}$= failure rate
$\lambda_s$ = “safe” failures
$\lambda_d$ = “dangerous” failures
$\lambda_{dd}$ = detectable “dangerous” failures
$\lambda_{du}$ = undetectable “dangerous” failures

I will be discussing some of these variables in more detail in a later part of the series when I delve into Diagnostic Coverage, so don’t worry about them too much just yet.

## Getting to MTTFD

Since we can now start to deal with the failure rate data mathematically, we can start to do some calculations about expected lifetime of a component or a system. That expected, or probable, lifetime is what definition 3.1.25 was on about, and is what we call MTTFD.

MTTFD is the time in years over which the probability of failure is relatively constant. If you look at a typical failure rate curve, called a “bathtub curve” due to its resemblance to the profile of a nice soaker tub, the MTTFD is the flatter portion of the curve between the end of the infant mortality period and the wear-out period at the end of life. This part of the curve is the portion assumed to be included in the “mission time” for the product. ISO 13849-1 assumes the mission time for all machinery is 20 years [1, 4.5.4] and [1, Cl. 10].

ISO 13849-1 provides us with guidance on how MTTFD relates to the determination of the PL in [1, Cl. 4.5.2]. MTTFD is further grouped into three bands as shown in [1, Table 4].

The notes for this table are important as well. Since you can’t read the notes particularly well in the table above, I’ve reproduced them here:

NOTE 1 The choice of the MTTFD ranges of each channel is based on failure rates found in the field as state-of-the-art, forming a kind of logarithmic scale fitting to the logarithmic PL scale. An MTTFD value of each channel less than three years is not expected to be found for real SRP/CS since this would mean that after one year about 30 % of all systems on the market will fail and will need to be replaced. An MTTFD value of each channel greater than 100 years is not acceptable because SRP/CS for high risks should not depend on the reliability of components alone. To reinforce the SRP/CS against systematic and random failure, additional means such as redundancy and testing should be required. To be practicable, the number of ranges was restricted to three. The limitation of MTTFD of each channel values to a maximum of 100 years refers to the single channel of the SRP/CS which carries out the safety function. Higher MTTFD values can be used for single components (see Table D.1).

NOTE 2 The indicated borders of this table are assumed within an accuracy of 5%.

The standard then tells us to select the MTTFD using a simple hierarchy [1, 4.5.2]:

For the estimation ofMTTFD of a component, the hierarchical procedure for finding data shall be, in the order given:

a) use manufacturer’s data;
b) use methods in Annex C and Annex D;
c) choose 10 years.

Why ten years? Ten years is half of the assumed mission lifetime of 20 years. More on mission lifetime in a later post.

Looking at [1, Annex C.2], you will find the “Good Engineering Practices” method for estimating MTTFD, presuming the manufacturer has not provided you with that information. ISO 13849-2 [2] has some reference tables that provide some general MTTFD values for some kinds of components, but not every part that exists can be listed. How can we deal with parts not listed? [1, Annex C.4] provides us with a calculation method for estimating MTTFD for pneumatic, mechanical and electromechanical components.

### Calculating MTTFD for pneumatic, mechanical and electromechanical components

I need to introduce you to a few more variables before we look at how to calculate MTTFD for a component.

Variables
Variable Description
B10 Number of cycles until 10% of the components fail (for pneumatic and electromechanical components)
B10D Number of cycles until 10% of the components fail dangerously (for pneumatic and electromechanical components)
T10D the mean time until 10% of the components fail dangerously
hop is the mean operation time, in hours per day;
dop is the mean operation time, in days per year;
tcycle is the mean operation time between the beginning of two successive cycles of the component. (e.g., switching of a valve) in seconds per cycle.
s seconds
h hours
a years

Knowing a few details we can calculate the MTTFD using [1, Eqn C.1]. We need to know the following parameters for the application:

• B10D
• hop
• dop
• tcycle

In order to use [1, Eqn. C.1], we need to first calculate nop, using [1, Eqn. C.2]:

We may also need one more calculation, [1, Eqn. C.4]:

## Example Calculation [1, C.4.3]

For a pneumatic valve, a manufacturer determines a mean value of 60 million cycles as B10D. The valve is used for two shifts each day on 220 operation days a year. The mean time between the beginning of two successive switching of the valve is estimated as 5 s. This yields the following values:

• dop of 220 days per year;
• hop of 16 h per day;
• tcycle of 5 s per cycle;
• B10D of 60 million cycles.

Doing the math, we get:

So there you have it, at least for a fairly simple case. There are more examples in ISO 13849-1, and I would encourage you to work through them. You can also find a wealth of examples in a report produced by the BGIA in Germany, called the Functional safety of machine controls (BGIA Report 2/2008e) [16]. The download for the report is linked from the reference list at the end of this article. If you are a SISTEMA user, there are lots of examples in the SISTEMA Cookbooks, and there are example files available so that you can see how to assemble the systems in the software.

The next part of this series covers Diagnostic Coverage (DC), and the average DC for multiple safety functions in a system, DCavg.

In case you missed the first part of the series, you can read it here.

## Book List

Here are some books that I think you may find helpful on this journey:

[0.2]  Electromagnetic Compatibility for Functional Safety, 1st ed. Stevenage, UK: The Institution of Engineering and Technology, 2008.

## References

Note: This reference list starts in Part 1 of the series, so “missing” references may show in other parts of the series. Included in the last post of the series is the complete reference list.

[15]    “The bathtub curve and product failure behavior part 1 of 2”, Findchart.co, 2017. [Online]. Available: http://findchart.co/download.php?aHR0cDovL3d3dy53ZWlidWxsLmNvbS9ob3R3aXJlL2lzc3VlMjEvaHQyMV8xLmdpZg. [Accessed: 03- Jan- 2017].

[16]   “Functional safety of machine controls – Application of EN ISO 13849 (BGIA Report 2/2008e)”, dguv.de, 2017. [Online]. Available: http://www.dguv.de/ifa/publikationen/reports-download/bgia-reports-2007-bis-2008/bgia-report-2-2008/index-2.jsp. [Accessed: 2017-01-04].