Consider an expensive part with a reliability of 966 If the

Consider an expensive part with a reliability of 96.6%. If the part fails, it will cost the firm $12,000.

        a. What is the expected failure cost per part?

        b. On each part, a rather unreliable backup can be installed that has a reliability of just 30%. What is the maximum amount that the firm should be willing to pay per part to install the backup? Support your answer.

        c. Suppose that a second 30% reliable backup part could be installed, so that if both the original and the first backup part fail, then the second backup part will be used. If that second backup part costs $100, should it be installed? Support your answer.

Solution

a)

expected failure cost = failure cost * probability of failure

= 12000 * (1-96.6%)

= 408

b)

new system reliability = 1 - ((1-reliability original)*(1-reliabilty backup))

= 1 - ( (1-96.6%)*(1-30%))

= 97.62%

expected failure cost =(1- 0.9762%) * backup cost = 408

=>

backup cost = 17142.86

c)

expected failure cost second part =(1- 0.9762%) * 100 =2.38

expected failure cost of system = 408 -2.38 = 405.62

yes they should buy the part