Question

4. An electrical system consists of 3 components (C1, C2 and C3) functioning independently, and are set in parallel layout. The failure density of each component is given as below: ?(?) = { 3? ^−3? , ? > 0

0 , ??ℎ??????

where X is in years.

(a) Calculate the probability that any one component will fail in less than 3/4 years.

(b) Write the complete failure density for the model appropriate for the system if all the components fail and  if any two of the components fail.

(c) Calculate the probability that the system fails in less than 1/ 4 years when any two of the components fail in less than 1/4 years.

Answer 1

Let be the life time of the component ,

(a)

(b)

CDF of any two component failing at time t is:

PDF of any two component failing at time is:

(c)