Question

Rick Wing, salesperson for Wave Soldering Systems, Inc. (WSSI), has provided you with a proposal for improving the temperature control on your present machine. The machine uses a hot-air knife to cleanly remove excess solder from printed circuit boards; this is a great concept, but the hot-air temperature control lacks reliability. According to Wing, engineers at WSS1 have improved the reliability of the critical temperature controls, The new system still has the four sensitive integrated circuits controlling the temperature, but the new machine has a backup for each. The four integrated circuits have reliabilities of .90, .92, .94, and .96. The four backup circuits all have a reliability of .90.

a) What is the reliability of the new temperature controller?
b) If you pay a premium. Wing says he can improve all four of the backup units to .93. What is the reliability of this option?

Answer 1

a) 0.97

b) 0.98

Step-by-step explanation:

a) Determine the reliability of the new temperature controller

given that :

R1 = 0.90, R'1 = 0.90,

R2 = 0.92, R'2 = 0.90,

R3 = 0.94, R'3 = 0.90,

R4 = 0.96, R'4 = 0.90

Rc ( reliability of new temperature controller ) = 0.97

detailed solution is attached below

b) what is the reliability of the new temperature controller when there is an improvement

hence :

R1 = 0.90, R'1 = 0.93

R2 = 0.92, R'2 = 0.93

R3 = 0.94, R'3 = 0.93

R4 = 0.96, R'4 = 0.93

hence Rc = ( reliability of newly improved temperature controller ) = 0.98

detailed solution is attached below

NOTE : R' = backup