Formulas

The SIL Master module performs hardware integrity analysis according to the following standards:

• IEC 61508:2010
• IEC 61508:1998 (Obsolete)
• ISA TR84.00.02:2022
• VDE/VDI 2180:2019
• PFD formulas

IEC 61508:2010 formulas

SIL Master can perform PFDavg and PFH calculations according to IEC 61508:2010.

1oo1 Formulas

1oo2 Formulas

1oo2D Formulas

2oo2 Formulas

2oo3 Formulas

Supporting formulas

ISA TR84.00.02:2022 formulas

SIL Master can perform PFD, PFH and STR calculations according to ISA TR84. The formulas use are coming directly from this technical report.

PFD Formulas

where

• DC is the diagnostic coverage - parameter from device, calculated or given
• DI is the diagnostic interval - is a parameter on subsystem level (hours)
• TI is the proof test interval - is a parameter on subsystem level (hours)

and




According to the TR84 document you provided, the definitions for N, M, and R in the context of the formula used for calculating the probability of failure on demand (PFDavg) are as follows:

• N refers to the total number of devices in the voting configuration. This represents the full set of redundant elements being considered for failure or success.
• M represents the minimum number of devices out of the total N devices that must operate correctly for the system to be considered successful. This is often referred to as M-out-of-N voting logic (e.g., 2oo3 means 2 out of 3 must work).
• R represents the number of common-cause failures, which are addressed in the equation by considering failure dependencies across devices. R=N−M+1

PFH Formulas

The following subsystems can be calculated with PFH formulas: 1oo1, 1oo2, 1oo3, 2oo2, 2oo3, 2oo2

STR formulas

VDI/VDE 2180:2019 formulas

SIL master can perform PFD calculations according to VDI/VDE 2180:2019. The formulas use are coming directly from this standard.

PFD Formulas

The following subsystems can be calculated with the PFD formulas: 1oo1, 1oo2, 1oo3, 2oo2, 2oo3, 3oo3

Formulas based on PFD1oo1

When you have a device without failure rates, but with a PFD value then we can still use this device to calculate PFD values for other architectures. We use the following formulas:

PFD1oo1

Select a device that has a PFD value or calculate PFD based on the failure rates.

PFD1oo2 and PFD1oo2D

We use the following formula:

PFD1oo2 and PFD1oo2D

We use the following formula:

PFD1oo3

We use the following formula:

PFD2oo3

We use the following formula:

PFD3oo3

We use the following formula:

PFD2oo4

We use the following formula: