National University of Singapore

ST 3247

ST3247 Semester II, 2022/2023
Tutorial 9
1. A Weibull distribution is commonly used to model a failure time random variable. It has two param-
eters: a and b, and the pdf is given by:
f (x) = axa−1
ba e−(x/b)a
for x > 0. The support of this distribution is [0, ∞).
(a) Suggest how you can generate from f .
(b) Replace the F function in the repair model example with a Weibull distribution with a = 1.5 and
b = 3. If you get stuck here, proceed by using rweibull(1,shape=1.5,scale=3).
(c) Replace the G function with an Exp(1) random variable.
(d) If our factory needs 15 machines to be in operation, create a plot that estimates the time until
crash for 5,6, . . . , 15 spares. For each scenario, simulate 1000 times. Include 90% confidence
interval limits in your plot.
Note: There is no basic R function that plots confidence interval limits for you. You may look
around for packages that do; or simply plot the poi