Process design often follows this pattern in practice:

1. Draw up P&ID’s and add instrumentation, safety functions and alarms
2. Perform HAZOP
3. Change P&ID’s
4. Perform SIL allocation study
5. Wait….
6. Calculate probabilities for failure on demand for safety functions with SIL requirements
7. Realize this is not going to work
8. Back to 3

Instead of doing this – which is very expensive – we should calculate the probability for failure on demand while designing the safety functions. This can be done in a number of ways, ranging from relatively coarse and simple to very involved and complex, like Petri nets and Monte Carlo simulations. For design evaluations, simple methods are usually good enough. The simplest of all may be the interpolation of pre-calculated results. Say someone compares a lot of architectures and failure rates and makes a gigantic table of PFD results for you – then you can just look it up. The good news is – somebody already did. You can find such tables in IEC 61508-6, Appendix B. This, we can of course use a spreadsheet to do, like in the example below – no fancy software needed in other words.

Say you have a safety function with a sensor element with λ_DU = 4 x 10^-7, and a logic unit with λ_DU = 2 x 10^-7 and your final elements with λ_DU = 2.6 x 10^-7. You need to comply with a SIL 3 requirement. Using the lookup tables, we then quickly estimate that the PFD is approximately 1.03 x 10^-3. This is quite close to SIL 3 performance but since there is some uncertainty in play and we know the final element is usually the problem (it also has the highest failure rate) we opt for a 1oo2 configuration of the final element. Then we obtain 4.7 x 10^-4, which is well within a SIL 3 requirement. As a designer, you can do these type of estimates already at point 1) in the sequence above – and you will save yourself a lot of trouble, delays and costs due to changes later in your design project.

For a small fee of 20 USD you can download the spreadsheet used in this example, capable of performing many different PFD calculations for 1-year test intervals (including diagonistics, common cause failures and redundancies). Get it here: Spreadsheet for SIL Calculations.