Question

The reliability of a component is modelled by a two parameter Weibull distribution with a shape factor (β)
equal to 2, and scale factor (η) equal to 100 weeks. The reliability function (R(t)) as a function of time
(weeks) is:
?(?) = ?^-(t/η^{)^}β

a) Explain what the reliability function represents, and when it might be used? (1 mark)
b) If the component has survived for 20 weeks of operation, what is the probability that the
component will fail in the next 100 weeks?
c) How many actively redundant components (with identical reliability functions) of the one system
are required to ensure that the reliability of the system at 20 weeks of operation is greater than
0.9999?

Answer 1