Lambda-Tau Calculations
The Lambda-Tau method is an alternative way to analyse a fault tree. It can be used to determine availability or short-term reliability when the age of a component or system is unknown or indeterminate. Lambda-Tau calculations are very good to use in the case of a system that is well-maintained and routinely undergoes preventative maintenance. In such systems, the age of specific components is difficult to determine, or the components have reached steady-state behaviour.
There are various situations where Lambda-Tau calculations may be applied. In all these situations, Lambda signifies the failure rate of the system or component. Tau can represent the inspection interval, repair time or mission time of the system, depending on the type of model in use. Table 5-12 describes various Lambda-Tau models and their calculations.
Table 5-12. Lambda-Tau Models
Model
Description
Lambda Tau
This model approximates the probability of failure and asymptotic unavailability.
A = λτ
τ =mission time to MTTR
Average Unavailability (approximately)
This model approximates the average unavailability.
A =λτ/ 2
τ =time between tests (inspection interval)
Probability of Failure
This model uses Tau as the mission time.
A = 1 – exp{–λτ}
τ =mission time to MTTR
Asymptotic Unavailability
This model uses asymptotic behaviour.
A= λτ /(λτ + 1)
τ =MTTR
Average Unavailability
This models uses average unavailability over 0 and Tau.
A=1+ (exp{–λτ} – 1)/ λτ
τ =time between tests (inspection interval)