Question $1$

Priscilla Antwi is the audio engineer for Event Planners, a company noted for organising large

and high$-$profile events. She is considering improvement measures to enhance the quality of

sound during events. She has made enquires form Sweet Music located at the Achimota Mall

and was presented with three offers: JBL$,$ QSC and BOSE professional sound systems. All the

three sound systems consist of five separate components arranged in series with identical

reliabilities. The JBL system has component reliabilities of $0\mathrm{.}90$ and costs $C15,000.$ The QSC

system has component reliabilities of $0\mathrm{.}95$ and costs $C20,000,$ and the BOSE system has

component reliabilities of $0\mathrm{.}98$ and costs $C35,000.$ The cost of a failure during a performance

at an event is estimated at $C50,000.$

a$)$ Calculate the reliability of each sound system.

$(6$ marks$)$

b$)$ Calculate the cost of failure for each system.

$(9$ marks$)$

c$)$ Based on the cost of failure calculated in $($b$)$ above, which brand of professional live audio

system would you recommend?

$(1$ mark$)$

d$)$ Priscilla 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.

With the Plus configuration, due to financial constraints Priscilla is considering a choice

between the QSC and JBL professional systems. Which of these two systems would you

recommend to Priscilla on the basis of the cost of failure?