Extension of ISA TR84.00.02 PFD equations to KooN architectures

Simplified equations for PFD evaluation of the most used architectures are given in ISA TR84.00.02-2002 document. This paper introduces a generalization of those equations for applications to any KooN architecture. The meaning of each individual term in the derived equations is explained. To strengthen their validity, several comparisons are made between their results and those of a numerical integration model for PFD assessment. The results show that the values obtained with the generalized equations are very close to those of the numerical model, even for highly redundant configurations. Comparisons are also made with the analytical equations given in IEC 61508. It is argued that the ISA equations are conceptually more consistent than those of IEC 61508 even though the numerical differences between the results are not significant in most practical cases. Overall, the results indicate that the generalized KooN PFD equations derived here may be applied to systems with higher redundancy, thus partly contradicting suggestions made in the above ISA reference that such equations should only be used for the simplest configurations. Some specific practical situations to which they cannot be applied are also pointed out.