Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# Question 3¤

The following distributions have similar hazard functions with the parameters:

- Loglogistic with = 0.1206, = 5.878
- Pareto with = 0.1, = 0.05
- Lognormal with = 0.0001, = 6.569.

What is R(3) - R(2) for the loglogistic? Click on one of the options below, then click on "Check Answer".

-0.0047
-0.0056
-0.0078
-0.0082
None of these
Yes, that's right. R(t) = 1/(1 + t^) so in Excel you can calculate it with:
=(1/(1+5.878*3^0.1206) - 1/(1+5.878*2^0.1206)) which gives the answer -0.0056.
No, the answer is -0.0056. This is because R(t) = 1/(1 + t^) so in Excel you can calculate it with:
=(1/(1+5.878*3^0.1206) - 1/(1+5.878*2^0.1206)) which gives the answer -0.0056.
Note: Although the hazard functions can be similar as shown here, the reliabilities can be quite different. The extreme case is the Pareto where parameter does not appear in the hazard function.