Features
What is PFDavg?
Introduction
IEC61508 requires probabilistic evaluation of each set of equipment used to reduce risk in a safety related system. Different order of magnitude risk reduction levels are achieved depending on the average probability of failure on demand (often called average probability of dangerous failure). In practice, a number of different methods have been used to calculate this probability. Among the most popular are fault tree analysis, reliability block diagrams, simplified equations (derived using a number of different ways) and Markov models. For those who use Markov models, different solution techniques are used. A debate has existed in various circles about the appropriateness of various methods. A tutorial of the different methods is available in a text by Goble, reference 1. A good comparison of the different methods is stated by Rouvroye in reference 2.
The fundamental problem is that these different methods give results that vary by 2X+ for same set of input parameters.
What is PFDavg – unavailability or unreliability?
Part of the problem may be different interpretations of the meaning of PFDavg. Two fundamentally different ways to calculate the metric are described. Note that a number of assumptions are made. These are listed at the end of the paper.
The unreliability approach
In one method, an unreliability function is calculated as a function of time interval for a specified mission time usually equal to a “proof test” interval for industrial equipment. Then the function is “averaged” over the entire mission time.
This model is used for safety related systems with the assumption that the system is periodically inspected and tested. It is often assumed that the periodic test will detect all failed components and the system will be renewed to perfect condition. Therefore the unreliability function is perfect for the problem. It is further reasoned that the system may fail right after the inspection, right before the inspection or at any time in between. Therefore, PFDavg is the average value of the unreliability function plotted over the inspection period.
It is a well known equation for a single channel system with a constant failure rate that: Unreliability for a specified mission time, t: F(t) = 1 – e-λt. This is sometimes called Probability of Failure, PF. PF(t) = 1 – e-λt.