Question $4$:

a$)$ A lightweight component in an electrical assembly has a reliability of $0\mathrm{.}70.$ Provision

of two redundant units can be tolerated with no appreciable effect on weight

specifications. If two redundant units of the same component are installed, what will

be the compound reliability of the three?

b$)$ An assembly, through simplification, can be reduced from six components to three

components. The reliability of each of the six components is $0\mathrm{.}98.$ Presuming no

change in component reliabilities, what would be the change in the assembly

reliability with reduction of components?

Question $5$:

The monthly usage rate for a certain type of cemented carbide insert used in the

machine shop is averaging $1100$ units. The inserts cost $$4\mathrm{.}36$ each when ordered in

quantities over $500.$ It is estimated that it costs an average of $$60$ each time a batch of

inserts is ordered. The holding cost for this shop is based on using $25\%$ per year of the

cost of the item in inventory. What is the economic order quantity for this insert?

Question $6$:

A digital$-$to$-$analog converter $($DAC$)$ uses a reference voltage source of $10$ V and uses a

binary register with six$-$digit precision. In two successive sampling instants $0\mathrm{.}5$ s apart,

the data contained in the binary register are as follows:

The DAC uses a zero$-$order hold to maintain the voltage output between sampling

instants. Determine the voltage output during the sampling interval following instant t $.$