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# PFD Calculation – ProSET vs IEC 61508

Why does my Probability of Failure on Demand, PFD, calculated within ProSET® differ from how the standard tells me it is calculated?

There are various ways to calculate the Probability of Failure on Demand, such as using the IEC 61508 standard or by using ProSET® to calculate this for you.

## IEC 61508 formula

Based upon IEC 61508-6 B.3.2.2.1, as an example, for a simplex (i.e 1oo1 configuration) the Probability of Failure on Demand, or PFD,  is calculated using: Where: And:

λDU = Dangerous Undetected Failure Rate (per hour)
λDD = Dangerous Detected Failure Rate (per hour)
λD = λDD + λDU
T1 = Proof Testing Interval (hours)
MRT = Mean Repair Time (hours)
MTTR = Mean Time to Restoration (hours)

It can be seen from the IEC 61508 formula that the PFD is simple to calculate considering a few factors.

## ProSET® PFD Calculation

Although ProSET® considers these same factors, ProSET® also incorporates additional factors as part of the PFD calculation:

• Proof Test Coverage – allowing for imperfect proof testing to be taken into consideration i.e, that not all unrevealed failure modes are to be revealed during a proof test;
• Mission Time (i.e. Overhaul Period) – the time in which the equipment will be replaced or overhauled to an as-new condition allowing for the remaining proportion of the undetected failure modes not revealed during a proof test to be revealed.
• Periodic Automatic Testing – ProSET® allows you to consider Partial Stroke Testing in it’s calculation

In the IEC 61508 formula, it is being assumed that the proof test coverage is 100% effective, i.e that all undetected failure modes will be revealed when a proof testing is conducted. Mission time is not accounted for in the IEC 61508 formula since the proof test coverage is assumed to be completely effective at revealing unrevealed failures. These assumptions therefore allow for the IEC 61508 formula to be simplified into the current formula that is shown above.

By including these additional factors, the PFD calculations produced through ProSET® allow for a more detailed equation to be used and can lead to a variation between what the software achieves and what is calculated using the formula in IEC 61508.

The inclusion of these additional factors does not mean that one formula is incorrect against the other, but that ProSET can be used to build a more complete representation of your system.

The parameters mentioned above can be modified within ProSET® to provide a like for like comparison between the two formulas.