Omar Marquez is the audio engineer for Summer Musical Enterprises. The group is considering the purchase of a new sound system consisting of five separate components. The components are arranged in series with identical reliabilities. The Basic system with component reliabilities of 80% costs $1000, the Standard system with component reliabilities of 90% costs $2000, and the Professional system with component reliabilities of 99% costs $5000. The cost of a failure during a performance is $50,000.
a. Calculate the reliability of each system. Which system would you recommend?
b. Omar has learned that each system described above can also be purchased in a Plus configuration, where each component has an identical backup, for double the original cost. Which system would you recommend now?