Safety Instrumented Systems Verification: Practical Probabilistic Calculations

When the results of the analysis are examined, several of the main features of different architectures become apparent. Table F-14 compares the results. The availability parameter was added to the results. It is calculated with the equation
| 1oo1 | 1oo2 | 2oo2 | 1oo1D | 2oo3 | 2oo2D | 1oo2D | ||
|---|---|---|---|---|---|---|---|---|
| FT Equation | PFD | 0.00102877 | 0.00002159 | 0.00203696 | 0.00099864 | 0.00006719 | 0.00197731 | 0.00002093 |
| FT Equation | PFDavg | 0.00053821 | 0.00001110 | 0.00106565 | 0.00049932 | 0.00003515 | 0.00098865 | 0.00001031 |
| FT Equation | PFS | 0.00024226 | 0.00047967 | 0.00000528 | 0.00039715 | 0.00001583 | 0.00000889 | 0.00000917 |
| FT Equation | Availability | 0.99872898 | 0.99949874 | 0.99795776 | 0.99860421 | 0.99991697 | 0.99801380 | 0.99996990 |
| Markov Solution | PFD | 0.00102794 | 0.00002153 | 0.00203354 | 0.00099775 | 0.00006674 | 0.00197381 | 0.00002318 |
| Markov Solution | PFS | 0.00024195 | 0.00047898 | 0.00000524 | 0.00039660 | 0.00001665 | 0.00000882 | 0.00000882 |
| Markov Solution | Availability | 0.99873011 | 0.99949949 | 0.99796122 | 0.99860565 | 0.99991661 | 0.99801737 | 0.99996800 |
| Markov Solution | MTTF | 61874 | 49865 | 81543 | 60017 | 2008305 | 1250619 | 1267137 |
It is interesting to note that the fault tree results and the Markov results are similar for this set of parameters. The failure rates used in the examples are sufficiently small to allow the first order approximation to be reasonably accurate.
Looking at the Markov solutions, the 1oo2 architecture has the highest risk reduction factor (lowest PFD). The 2oo3 architecture has highest MTTF but the 1oo2D architecture has the highest availability. Both of these metrics indicate successful operation but show different views. The metrics indicate that the 2oo3 will have fewer system failures but will spend more time in a failed state.