Consider a product with two components in series (component A and component B). Component A has a reliability of 92%, while component B has a reliability of 87%. It is known that if the product fails, it will cost the company $1000. (Keep all reliability calculations to 4 decimals)
a) What is the system reliability and the expected failure cost per part?
b) You are trying to reduce the expected failure cost per part of the product, and you have three improvement options. For each of the three improvements: (1) find the system reliability and (2) find the total cost (failure + improvement) per part. Finally, which of the three improvements (if any) would you recommend?
i. Improvement 1: Add a 50% reliable backup for Component A. The backup costs $20 per part.
ii. Improvement 2: Add a 99% reliable backup for Component B. The backup costs $110 per part.
iii. Improvement 3: Add a backup for Component A and add a backup for Component B. Backups have same reliabilities and costs as in Improvements 1 & 2. Recommendation: