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The mean time between failures (MTBF, /) is often reported instead of the failure rate, as numbers such as "2,000 hours" are more intuitive than numbers such as "0.0005 per hour". However, this is only valid if the failure rate λ ( t ) {\displaystyle \lambda (t)} is actually constant over time, such as within the flat region of the bathtub curve.
For continuous operation, these change to the following, where PFH is probability of dangerous failure per hour. SIL PFH PFH (power) RRF 1 0.00001-0.000001
Annualized failure rate (AFR) gives the estimated probability that a device or component will fail during a full year of use. It is a relation between the mean time between failure ( MTBF ) and the hours that a number of devices are run per year.
These failure rates are quantified as the Probability of Dangerous Failure per hour, PFH d. The numeric values for PFH d are given in Annex K. The PL range for each band has a 5% tolerance. The PFH d covered by ISO 13849-1 range from the highest failure rate in PL a < 1 × 10 −4 to the lowest failure rate in PL e at ≥ 1 × 10 −8.
For example, three identical systems starting to function properly at time 0 are working until all of them fail. The first system fails after 100 hours, the second after 120 hours and the third after 130 hours. The MTBF of the systems is the average of the three failure times, which is 116.667 hours.
For a safety function operating in high demand or continuous mode of operation, SIL 1 is associated with a probability of dangerous failure limit of 10 −5 per hour while SIL 4 is associated with a probability of dangerous failure rate limit of 10 −9 per hour.
The 'bathtub curve' hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line). The bathtub curve is a particular shape of a failure rate graph.
average probability of failure on demand : High demand or continuous mode: probability of dangerous failure per hour : 1: ≥ 10 −2 to < 10 −1: ≥ 10 −6 to ...