Your organization must decide to purchase one of two possible systems. Both of the systems are currently three months old. Each system consists of the same three sub-components, all of which must be operational in order for the system to work.

Furthermore, two possible operating conditions may exist. The first operating condition is denoted by s1 and the second operating condition is denoted by s2. There is a 40% probability that s1 will exist and a 60% probability of s2. Within each potential operating condition, the reliability of each component is defined as either normally or exponentially distributed with associated parameters (in months) given in the table below:

System A:

	s1	s2	Replacement Cost
Component 1	Normal: = 3, = 0.5	Normal: = 4, = 0.5	$1,000
Component 2	Exponential: MTTF = 2	Exponential: MTTF = 3	$2,000
Component 3	Life = 4 months	Life = 6 months	$1,600

System B:

	s1	s2	Replacement Cost
Component 1	Normal: = 4, = 1	Normal: = 6, = 1	$1,500
Component 2	Exponential: MTTF = 3	Exponential: MTTF = 3	$2,500
Component 3	Life = 6 months	Life = 6 months	$1,800

a) What is the expected maintenance costs for each system over the next 12 months?

b) What is the probability of the first two components both surviving for the next 6 months for system 1? system 2?

c) Suppose that an alternative to using Component 2 was to replace it with a second "Component 1". What would be the probability that the two Component 1s would survive for 6 months for system 1? system 2?