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

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

The following subsystems can be calculated with the STR formulas: 1oo1, 1oo2, 1oo3, 2oo2, 2oo3, 3oo3, and 3oo4
image (386).png

where

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

2180 - PFD 1

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: