Average probability per flight

The objective of CS25.1309 is to ensure an acceptable safety level for equipment and systems as installed on the aeroplane. A logical and acceptable inverse relationship must exist between the Average Probability per Flight Hour and the severity of failure condition effects as shown in Fig. 2.3, such that ... 

Probability targets are normally expressed as a failure rate as opposed to an absolute probability of failure. For instance, CS25.1309 expresses probability targets based on the severity of the failure condition in "Average Probability per Flight Hour . This is easy to accomplish when all of the basic events are also expressed as a failure rate however, confusion can arise when some of the basic events are affected by time at risk or are dormant events that may lay in a failed state for many flights and only result in an issue when another failure or a specific circumstance occurs. 

Step 3 calculation of the average probability per flight of a failure condition... 

Calculate the probability of the failure condition by summing up the average probabilities per flight (during the relevant time) and divide it by the number of flights during that period. ... 

When using quantitative analyses to help determine compliance with EAR/CS 25.1309(b), these descriptions of the probability terms have become commonly accepted as aids to engineering judgement. They are expressed in terms of acceptable ranges for the average probability per flight hour. 

The probability per flight can then be calculated for the top-level event. To convert back to a failure rate, this number can simply be divided through by the average flight time to get back to an average probabiUty per flight hour. 

Dormant failures relate to nonactive failures, where the failure is not detectable. In this case, the probability for a flight cycle is the probability per flight hour multiplied by the check interval rather than the average flight time. The accepted equation actually uses half of the check interval, on the basis that the furthest you can be from knowing the state of the item is either half the check interval from the last checked state, or half the check interval from the future checked state. 

Safety-related malfunction (per flight hour) Average reaction time (hours) Probability of accident Affected fleet exposure... 

The desired intervals can be calculated via probabilistic assessment methods as follows if p = the probability of a dormant fault per flight hour and Tg = the duration between checks then the probability of the fault being present is P = pTg (or, more precisely P = 1 - e especially if Tg is large). So, the probability of a dormant fault depends on the elapsed time since it was last checked (i.e. it is ostensibly zero immediately after the check and pTg immediately before the next check, leading to 0 at Tg = MTBF. Thus, the average probability of a dormant fault will be P = V2pTg, or for very long check periods, P = V2(l - e p °). 

An interpretation of extreme improbabihty is also given. First, by a magic number 10" . This is a probability of failttre averaged per hom of flight. 

Civil aviation catastrophic accidents occur on average once every 1 million flying hours. The probability of these catastrophic accidents is p = 10 per hour. So, for a flight duration of four hours, it can be assumed that the probability of an aircraft crash is P = pT = 4 x 10 ... 

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