Suppose that the cumulative distribution function of the lifetime of a piece of operating equipment is given by F(t)  1  e0.6t  0.6te0.6t, where t is measured in years of continuous operation.

a. Determine the reliability function.

b. Determine the failure rate function.

c. What is the probability that this piece of equipment fails in the first year of operation?

d. What is the probability that this piece of equipment fails in the fifth year of operation?

e. What proportion of the equipment surviving four years fails in the fifth year?

(Calculate without using the failure rate function.)

f. Does r(4) closely approximate the answer to part (e)? Why or why not?

g. What proportion of the equipment surviving four years fails in the first month of the fifth year? (Calculate using the failure rate function.)