Safety Instrumented Systems Verification: Practical Probabilistic Calculations

Comparing Architectures

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


Table F.14: Architecture Calculation Results

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.

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