1. Modelling failure of a household refrigerator: The time to failure of a particular refrigerator type is represented by the following pdf: f(t)=0.003(10-t)2, which is valid within 0 t 10 yr, and f(t) = 0 elsewhere.

a. Determine the expression for R(t), and then calculate the reliability for the first year, t = 1.

b. If a 90% reliable refrigerator is required, calculate the refrigerator's Design Life corresponding to 0.90 reliability.

c. Write the expression for and obtain the failure rate function, (t), and state whether it is increasing or decreasing as t approaches infinity for this case.

d. To evaluate the reliability of this refrigerator, write the expression for and calculate the MTTF (mean time to failure).

e. Obtain the probability and thereby the % units of this refrigerator that are expected to survive its MTTF.

f. The refrigerator company has a 1-month warranty program. Write the expression for and obtain the probability that the refrigerator will fail during the first month.

g. Write the expression for and calculate the probability that the refrigerator will survive the 1-month warranty program. Then write the expression for and calculate the conditional probability that the refrigerator will survive the rest of the first year, given the probability that it will survive its warranty period of one month.