Consider an expensive part with a reliability of 89.8%. If the part fails, it will cost the firm $4800.

a. What is the expected failure cost per part?

b. Suppose you only have a single part, and engineers are looking at installing a backup for each part that would reduce the number of failures. Would it be better to (1) install a $380 backup that is 60% reliable, or (2) not install a backup at all?

c. On each part, a backup can be installed that costs $380. What is the minimum allowable reliability for the backup that would make installing it worthwhile?

Use the formulas below to aid in answering question 4).

1) Expected Failure Cost Per Part = (Cost of a failed part)(Probability of Failure)

2) Overall Expected Cost of Failures = (Demand)(Expected Failure Cost Per Part) 3) Reliability (with a backup) = 1 [P(1^st fails)P(2^nd fails)]

4) Failure Cost Per Part (with a backup) = (Cost of a failed part) (1 Reliability)

5) Total Cost of Improvement Plus Failure = [Cost to install a backup] + [Failure Cost Per Part (with a backup)]