## ISO 13849 – 1 Analysis — Part 6: CCF — Common Cause Failures

This entry is part 6 of 9 in the series How to do a 13849 – 1 ana­lys­is

# What is a Common Cause Failure?

There are two similar-​sounding terms that people often get con­fused: Common Cause Failure (CCF) and Common Mode Failure. While these two types of fail­ures sound sim­il­ar, they are dif­fer­ent. A Common Cause Failure is a fail­ure in a sys­tem where two or more por­tions of the sys­tem fail at the same time from a single com­mon cause. An example could be a light­ning strike that causes a con­tact­or to weld and sim­ul­tan­eously takes out the safety relay pro­cessor that con­trols the con­tact­or. Common cause fail­ures are there­fore two dif­fer­ent man­ners of fail­ure in two dif­fer­ent com­pon­ents, but with a single cause.

Common Mode Failure is where two com­pon­ents or por­tions of a sys­tem fail in the same way, at the same time. For example, two inter­pos­ing relays both fail with wel­ded con­tacts at the same time. The fail­ures could be caused by the same cause or from dif­fer­ent causes, but the way the com­pon­ents fail is the same.

Common-​cause fail­ure includes com­mon mode fail­ure, since a com­mon cause can res­ult in a com­mon man­ner of fail­ure in identic­al devices used in a sys­tem.

Here are the form­al defin­i­tions of these terms:

3.1.6 com­mon cause fail­ure CCF

fail­ures of dif­fer­ent items, res­ult­ing from a single event, where these fail­ures are not con­sequences of each oth­er

Note 1 to entry: Common cause fail­ures should not be con­fused with com­mon mode fail­ures (see ISO 12100:2010, 3.36). [SOURCE: IEC 60050?191-am1:1999, 04 – 23.] [1]

3.36 com­mon mode fail­ures

fail­ures of items char­ac­ter­ized by the same fault mode

NOTE Common mode fail­ures should not be con­fused with com­mon cause fail­ures, as the com­mon mode fail­ures can res­ult from dif­fer­ent causes. [lEV 191 – 04-​24] [3]

The “com­mon mode” fail­ure defin­i­tion uses the phrase “fault mode”, so let’s look at that as well:

fail­ure mode
DEPRECATED: fault mode
man­ner in which fail­ure occurs

Note 1 to entry: A fail­ure mode may be defined by the func­tion lost or oth­er state trans­ition that occurred. [IEV 192 – 03-​17] [17]

As you can see, “fault mode” is no longer used, in favour of the more com­mon “fail­ure mode”, so it is pos­sible to re-​write the common-​mode fail­ure defin­i­tion to read, “fail­ures of items char­ac­ter­ised by the same man­ner of fail­ure.”

# Random, Systematic and Common Cause Failures

Why do we need to care about this? There are three man­ners in which fail­ures occur: ran­dom fail­ures, sys­tem­at­ic fail­ures, and com­mon cause fail­ures. When devel­op­ing safety related con­trols, we need to con­sider all three and mit­ig­ate them as much as pos­sible.

Random fail­ures do not fol­low any pat­tern, occur­ring ran­domly over time, and are often brought on by over-​stressing the com­pon­ent, or from man­u­fac­tur­ing flaws. Random fail­ures can increase due to envir­on­ment­al or process-​related stresses, like cor­ro­sion, EMI, nor­mal wear-​and-​tear, or oth­er over-​stressing of the com­pon­ent or sub­sys­tem. Random fail­ures are often mit­ig­ated through selec­tion of high-​reliability com­pon­ents [18].

Systematic fail­ures include common-​cause fail­ures, and occur because some human beha­viour occurred that was not caught by pro­ced­ur­al means. These fail­ures are due to design, spe­cific­a­tion, oper­at­ing, main­ten­ance, and install­a­tion errors. When we look at sys­tem­at­ic errors, we are look­ing for things like train­ing of the sys­tem design­ers, or qual­ity assur­ance pro­ced­ures used to val­id­ate the way the sys­tem oper­ates. Systematic fail­ures are non-​random and com­plex, mak­ing them dif­fi­cult to ana­lyse stat­ist­ic­ally. Systematic errors are a sig­ni­fic­ant source of common-​cause fail­ures because they can affect redund­ant devices, and because they are often determ­in­ist­ic, occur­ring whenev­er a set of cir­cum­stances exist.

Systematic fail­ures include many types of errors, such as:

• Manufacturing defects, e.g., soft­ware and hard­ware errors built into the device by the man­u­fac­turer.
• Specification mis­takes, e.g. incor­rect design basis and inac­cur­ate soft­ware spe­cific­a­tion.
• Implementation errors, e.g., improp­er install­a­tion, incor­rect pro­gram­ming, inter­face prob­lems, and not fol­low­ing the safety manu­al for the devices used to real­ise the safety func­tion.
• Operation and main­ten­ance, e.g., poor inspec­tion, incom­plete test­ing and improp­er bypassing [18].

Diverse redund­ancy is com­monly used to mit­ig­ate sys­tem­at­ic fail­ures, since dif­fer­ences in com­pon­ent or sub­sys­tem design tend to cre­ate non-​overlapping sys­tem­at­ic fail­ures, redu­cing the like­li­hood of a com­mon error cre­at­ing a common-​mode fail­ure. Errors in spe­cific­a­tion, imple­ment­a­tion, oper­a­tion and main­ten­ance are not affected by diversity.

Fig 1 below shows the res­ults of a small study done by the UK’s Health and Safety Executive in 1994 [19] that sup­ports the idea that sys­tem­at­ic fail­ures are a sig­ni­fic­ant con­trib­ut­or to safety sys­tem fail­ures. The study included only 34 sys­tems (n=34), so the res­ults can­not be con­sidered con­clus­ive. However, there were some start­ling res­ults. As you can see, errors in the spe­cific­a­tion of the safety func­tions (Safety Requirement Specification) res­ul­ted in about 44% of the sys­tem fail­ures in the study. Based on this small sample, sys­tem­at­ic fail­ures appear to be a sig­ni­fic­ate source of fail­ures.

# Handling CCF in ISO 13849 – 1

Now that we under­stand WHAT Common-​Cause Failure is, and WHY it’s import­ant, we can talk about HOW it is handled in ISO 13849 – 1. Since ISO 13849 – 1 is inten­ded to be a sim­pli­fied func­tion­al safety stand­ard, CCF ana­lys­is is lim­ited to a check­list in Annex F, Table F.1. Note that Annex F is inform­at­ive, mean­ing that it is guid­ance mater­i­al to help you apply the stand­ard. Since this is the case, you could use any oth­er means suit­able for assess­ing CCF mit­ig­a­tion, like those in IEC 61508, or in oth­er stand­ards.

Table F.1 is set up with a series of mit­ig­a­tion meas­ures which are grouped togeth­er in related cat­egor­ies. Each group is provided with a score that can be claimed if you have imple­men­ted the mit­ig­a­tions in that group. ALL OF THE MEASURES in each group must be ful­filled in order to claim the points for that cat­egory. Here’s an example:

In order to claim the 20 points avail­able for the use of sep­ar­a­tion or segreg­a­tion in the sys­tem design, there must be a sep­ar­a­tion between the sig­nal paths. Several examples of this are giv­en for clar­ity.

Table F.1 lists six groups of mit­ig­a­tion meas­ures. In order to claim adequate CCF mit­ig­a­tion, a min­im­um score of 65 points must be achieved. Only Category 2, 3 and 4 archi­tec­tures are required to meet the CCF require­ments in order to claim the PL, but without meet­ing the CCF require­ment you can­not claim the PL, regard­less of wheth­er the design meets the oth­er cri­ter­ia or not.

One final note on CCF: If you are try­ing to review an exist­ing con­trol sys­tem, say in an exist­ing machine, or in a machine designed by a third party where you have no way to determ­ine the exper­i­ence and train­ing of the design­ers or the cap­ab­il­ity of the company’s change man­age­ment pro­cess, then you can­not adequately assess CCF [8]. This fact is recog­nised in CSA Z432-​16 [20], chapter 8. [20] allows the review­er to simply veri­fy that the archi­tec­tur­al require­ments, exclus­ive of any prob­ab­il­ist­ic require­ments, have been met. This is par­tic­u­larly use­ful for engin­eers review­ing machinery under Ontario’s Pre-​Start Health and Safety require­ments [21], who are fre­quently work­ing with less-​than-​complete design doc­u­ment­a­tion.

In case you missed the first part of the series, you can read it here. In the next art­icle in this series, I’m going to review the pro­cess flow for sys­tem ana­lys­is as cur­rently out­lined in ISO 13849 – 1. Watch for it!

# 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. The com­plete ref­er­ence list is included in the last post of the series.

[17]      “fail­ure mode”, 192−03−17, International Electrotechnical Vocabulary. IEC International Electrotechnical Commission, Geneva, 2015.

[18]      M. Gentile and A. E. Summers, “Common Cause Failure: How Do You Manage Them?,” Process Saf. Prog., vol. 25, no. 4, pp. 331 – 338, 2006.

[19]     Out of Control — Why con­trol sys­tems go wrong and how to pre­vent fail­ure, 2nd ed. Richmond, Surrey, UK: HSE Health and Safety Executive, 2003.

## ISO 13849 – 1 Analysis — Part 5: Diagnostic Coverage (DC)

This entry is part 5 of 9 in the series How to do a 13849 – 1 ana­lys­is

# What is Diagnostic Coverage?

Understanding Diagnostic Coverage (DC) as it is used in ISO 13849 – 1 [1] is crit­ic­al to ana­lys­ing the design of any safety func­tion assessed using this stand­ard. In case you missed a pre­vi­ous part of the series, you can read it here.

In the last instal­ment of this series dis­cuss­ing MTTFD, I brought up the fact that everything fails even­tu­ally, and so everything has a nat­ur­al fail­ure rate. The bathtub curve shown at the top of this post shows a typ­ic­al fail­ure rate curve for most products. Failure rates tell you the aver­age time (or some­times the mean time) it takes for com­pon­ents or sys­tems to fail. Failure rates are expressed in many ways, MTTFD and PFHd being the ways rel­ev­ant to this dis­cus­sion of ISO 13849 ana­lys­is. MTTFis giv­en in years, and PFHd is giv­en in frac­tion­al hours (1/​h). As a remind­er, PFHd stands for “Probability of dan­ger­ous Failure per Hour”.

Three of the stand­ard archi­tec­tures include auto­mat­ic dia­gnost­ic func­tions, Categories 2, 3 and 4. As soon as we add dia­gnostics to the sys­tem, we need to know what faults the dia­gnostics can detect and how many of the dan­ger­ous fail­ures rel­at­ive to the total num­ber of fail­ures that rep­res­ents. Diagnostic Coverage (DC) rep­res­ents the ratio of dan­ger­ous fail­ures that can be detec­ted to the total dan­ger­ous fail­ures that could occur, expressed as a per­cent­age. There will be some fail­ures that do not res­ult in a dan­ger­ous fail­ure, and those fail­ures are excluded from DC because we don’t need to worry about them – if they occur, the sys­tem will not fail into a dan­ger­ous state.

Here’s the form­al defin­i­tion from [1]:

3.1.26 dia­gnost­ic cov­er­age (DC)

meas­ure of the effect­ive­ness of dia­gnostics, which may be determ­ined as the ratio between the fail­ure rate of detec­ted dan­ger­ous fail­ures and the fail­ure rate of total dan­ger­ous fail­ures

Note 1 to entry: Diagnostic cov­er­age can exist for the whole or parts of a safety-​related sys­tem. For example, dia­gnost­ic cov­er­age could exist for sensors and/​or logic sys­tem and/​or final ele­ments. [SOURCE: IEC 61508 – 4:1998, 3.8.6, mod­i­fied.]

That brings up two oth­er related defin­i­tions that need to be kept in mind [1]:

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.]

and the most import­ant one [1]:

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-​to- func­tion state.

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

Just as a remind­er, SRP/​CS stands for “safety-​related parts of con­trol sys­tems”.

## Failure Math

### Failure Rate Data Sources

To do any cal­cu­la­tions, we need data, and this is true for fail­ure rates as well. ISO 13849 – 1 provides some tables in the annexes that list some com­mon types of com­pon­ents and their asso­ci­ated fail­ure rates, and there are more fail­ure rate tables in ISO 13849 – 2. A word of cau­tion here: Do not mix sources of fail­ure rate data, as the con­di­tions under which that data is true won’t match the data in ISO 13849. There are a few good sources of fail­ure rate data out there, for example, MIL-​HDBK-​217, Reliability Prediction of Electronic Equipment [15], as well as the data­base main­tained by Exida. In any case, use a single source for your fail­ure rate data.

### Failure Rate Variables

IEC 61508 [7] defines a num­ber of vari­ables related to fail­ure rates. The lower­case Greek let­ter lambda, $\lambda$, is used to denote fail­ures.

The com­mon vari­able des­ig­na­tions used are:

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

### Calculating DC

Of these vari­ables, we only need to con­cern ourselves with $\lambda_d$, $\lambda_{dd}$ and $\lambda_{du}$. To under­stand how these vari­ables are used, we can express their rela­tion­ship as

$\lambda_d=\lambda_{dd}+\lambda_{du}$

Following on that idea, the Diagnostic Coverage can be expressed as a per­cent­age like this:

$DC\%=\frac{\lambda_{dd}}{\lambda_d}\times 100$

## Determining DC%

If you want to actu­ally cal­cu­late DC%, you have some work ahead of you. Rather than going into the details here, I am going to refer you hard­core types to IEC 61508 – 2, Functional safety of electrical/​electronic/​programmable elec­tron­ic safety-​related sys­tems – Part 2: Requirements for electrical/​electronic/​programmable elec­tron­ic safety-​related sys­tems. This stand­ard goes into some depth on how to determ­ine fail­ure rates and how to cal­cu­late the “Safe Failure Fraction,” a num­ber which is related to DC but is not the same.

For every­one else, the good news is that you can use the table in Annex E to estim­ate the DC%. It’s worth not­ing here that Annex E is “Informative.” In standards-​speak, this means that the inform­a­tion in the annex is not part of the “norm­at­ive” text, which means that it is simply inform­a­tion to help you use the norm­at­ive part of the stand­ard. The design must con­form to the require­ments in the norm­at­ive text if you want to claim con­form­ity to the stand­ard. The fact that [1, Annex E] is inform­at­ive gives you the option to cal­cu­late the DC% value rather than select­ing it from Table E.1. Using the cal­cu­lated value would not viol­ate the require­ments in the norm­at­ive text.

If you are using IFA SISTEMA [16] to do the cal­cu­la­tions for you, you will find that the soft­ware lim­its you to select­ing a single DC meas­ure from Table E.1, and this prin­ciple applies if you are doing the cal­cu­la­tions by hand too. Only one item from Table E.1 can be selec­ted for a giv­en safety func­tion.

## Ranking DC

Once you have determ­ined the DC for a safety func­tion, you need to com­pare the DC value against [1, Table 5] to see if the DC is suf­fi­cient for the PLr you are try­ing to achieve. Table 5 bins the DC res­ults into four ranges. Just like bin­ning the PFHd val­ues into five ranges helps to pre­vent pre­ci­sion bias in estim­at­ing the prob­ab­il­ity of fail­ure of the com­plete sys­tem or safety func­tion, the ranges in Table 5 helps to pre­vent pre­ci­sion bias in the cal­cu­lated or selec­ted DC val­ues.

If the DC value was high enough for the PLr, then you are done with this part of the work. If not, you will need to go back to your design and add addi­tion­al dia­gnost­ic fea­tures so that you can either select a high­er cov­er­age from [1, Table E.1] or cal­cu­late a high­er value using [14].

## Multiple safety functions

When you have mul­tiple safety func­tions that make up a com­plete safety sys­tem, for example, an emer­gency stop func­tion and a guard inter­lock­ing func­tion, the DC val­ues need to be aver­aged to determ­ine the over­all DC for the com­plete sys­tem. [1, Annex E] provides you with a meth­od to do this in Equation E.1.

Plug in the val­ues for MTTFD and DC for each safety func­tion, and cal­cu­late the res­ult­ing DCavg value for the com­plete sys­tem.

That’s it for this art­icle. The next part will cov­er Common Cause Failures (CCF). Look for it on 20-​Mar-​17!

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.

[16]     “IFA – Practical aids: Software-​Assistent SISTEMA: Safety Integrity – Software Tool for the Evaluation of Machine Applications”, Dguv​.de, 2017. [Online]. Available: http://​www​.dguv​.de/​i​f​a​/​p​r​a​x​i​s​h​i​l​f​e​n​/​p​r​a​c​t​i​c​a​l​-​s​o​l​u​t​i​o​n​s​-​m​a​c​h​i​n​e​-​s​a​f​e​t​y​/​s​o​f​t​w​a​r​e​-​s​i​s​t​e​m​a​/​i​n​d​e​x​.​jsp. [Accessed: 30- Jan- 2017].

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

This entry is part 4 of 9 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)
T life­time of the com­pon­ent
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://​find​chart​.co/​d​o​w​n​l​o​a​d​.​p​h​p​?​a​H​R​0​c​D​o​v​L​3​d​3​d​y​5​3​Z​W​l​i​d​W​x​s​L​m​N​v​b​S​9​o​b​3​R​3​a​X​J​l​L​2​l​z​c​3​V​l​M​j​E​v​a​H​Q​y​M​V​8​x​L​m​d​pZg. [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/​i​f​a​/​p​u​b​l​i​k​a​t​i​o​n​e​n​/​r​e​p​o​r​t​s​-​d​o​w​n​l​o​a​d​/​b​g​i​a​-​r​e​p​o​r​t​s​-​2​0​0​7​-​b​i​s​-​2​0​0​8​/​b​g​i​a​-​r​e​p​o​r​t-2 – 2008/index-2.jsp. [Accessed: 2017-​01-​04].